Model Analysis
Nikhil Gupta
2019-02-09 15:24:48
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## loaded via a namespace (and not attached):
## [1] compiler_3.5.1 magrittr_1.5 tools_3.5.1 htmltools_0.3.6
## [5] yaml_2.2.0 Rcpp_1.0.0 stringi_1.2.4 rmarkdown_1.11
## [9] knitr_1.20 stringr_1.3.1 digest_0.6.18 evaluate_0.12User Inputs
output.var = params$output.var
transform.abs = params$transform.abs
log.pred = params$log.pred
eda = params$eda
algo.forward = params$algo.forward
algo.backward = params$algo.backward
algo.stepwise = params$algo.stepwise
algo.LASSO = params$algo.LASSO
algo.LARS = params$algo.LARS
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 9
## $ output.var : chr "y3"
## $ transform.abs: logi FALSE
## $ log.pred : logi FALSE
## $ eda : logi FALSE
## $ algo.forward : logi FALSE
## $ algo.backward: logi FALSE
## $ algo.stepwise: logi TRUE
## $ algo.LASSO : logi FALSE
## $ algo.LARS : logi FALSE# Setup Labels
# alt.scale.label.name = Alternate Scale variable name
# - if predicting on log, then alt.scale is normal scale
# - if predicting on normal scale, then alt.scale is log scale
if (log.pred == TRUE){
label.names = paste('log.',output.var,sep="")
alt.scale.label.name = output.var
}
if (log.pred == FALSE){
label.names = output.var
alt.scale.label.name = paste('log.',output.var,sep="")
}Prepare Data
Read and Clean Features
features = read.csv("../../Data/features.csv")
#str(features) Checking correlations to evaluate removal of redundant features
corr.matrix = round(cor(features[sapply(features, is.numeric)]),2)
# filter out only highly correlated variables
threshold = 0.6
corr.matrix.tmp = corr.matrix
diag(corr.matrix.tmp) = 0
high.corr = apply(abs(corr.matrix.tmp) >= threshold, 1, any)
high.corr.matrix = corr.matrix.tmp[high.corr, high.corr]
DT::datatable(corr.matrix)DT::datatable(high.corr.matrix)Feature Names
feature.names = colnames(features)
drops <- c('JobName')
feature.names = feature.names[!(feature.names %in% drops)]
#str(feature.names)Read and Clean Labels
labels = read.csv("../../Data/labels.csv")
#str(labels)
labels = labels[,c("JobName", output.var)]
summary(labels)## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.21
## Job_00003: 1 Median :123.99
## Job_00004: 1 Mean :125.36
## Job_00005: 1 3rd Qu.:131.06
## Job_00006: 1 Max. :193.73
## (Other) :9994 NA's :2497Merge Datasets
data <- merge(features, labels, by = 'JobName')
drops <- c('JobName')
data = data[,(!colnames(data) %in% drops)]
#str(data)Transformations
if (transform.abs == TRUE){
data[,label.names] = 10^(data[,label.names]/20)
data = filter(data, y3 < 1E7)
}
#str(data)
if (log.pred == TRUE){
data[label.names] = log(data[alt.scale.label.name],10)
drops = c(alt.scale.label.name)
data = data[!(names(data) %in% drops)]
}
#str(data)Remove NA Cases
data = data[complete.cases(data),]Exploratory Data Analysis
Check correlation of Label with Featires
if (eda == TRUE){
corr.to.label =round(cor(dplyr::select(data,-one_of(label.names)),dplyr::select_at(data,label.names)),4)
DT::datatable(corr.to.label)
}Multicollinearity - VIF
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,feature.names)) %>% arrange(desc(VIF))
head(vifDF,10)
}Scatterplots
panel.hist <- function(x, ...)
{
usr <- par("usr"); on.exit(par(usr))
par(usr = c(usr[1:2], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col = "cyan", ...)
}if (eda == TRUE){
histogram(data[ ,label.names])
#hist(data[complete.cases(data),alt.scale.label.name])
}# https://stackoverflow.com/questions/24648729/plot-one-numeric-variable-against-n-numeric-variables-in-n-plots
ind.pairs.plot <- function(data, xvars=NULL, yvar)
{
df <- data
if (is.null(xvars)) {
xvars = names(data[which(names(data)!=yvar)])
}
#choose a format to display charts
ncharts <- length(xvars)
for(i in 1:ncharts){
plot(df[,xvars[i]],df[,yvar], xlab = xvars[i], ylab = yvar)
}
}
if (eda == TRUE){
ind.pairs.plot(data, feature.names, label.names)
}
#
# pl <- ggplot(data, aes(x=x18, y = y3))
# pl2 <- pl + geom_point(aes(alpha = 0.1)) # default color gradient based on 'hp'
# print(pl2)Feature Engineering
if(eda ==FALSE){
# x18 may need transformations
plot(data[,'x18'], data[,label.names], main = "Original Scatter Plot vs. x18", ylab = label.names, xlab = 'x18')
plot(sqrt(data[,'x18']), data[,label.names], main = "Original Scatter Plot vs. sqrt(x18)", ylab = label.names, xlab = 'sqrt(x18)')
# transforming x18
data$sqrt.x18 = sqrt(data$x18)
data = dplyr::select(data,-one_of('x18'))
# what about x7, x9?
# x11 looks like data is at discrete points after a while. Will this be a problem?
}
Modeling
Train Test Split
data = data[sample(nrow(data)),] # randomly shuffle data
split = sample.split(data[,label.names], SplitRatio = 0.8)
data.train = subset(data, split == TRUE)
data.test = subset(data, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
plot(predict(model,train),r.student,
ylab="Student Residuals", xlab="Predicted Values",
main="Student Residual Plot")
abline(0, 0)
plot(predict(model, train),r.standard,
ylab="Standard Residuals", xlab="Predicted Values",
main="Standard Residual Plot")
abline(0, 0)
abline(2, 0)
abline(-2, 0)
# Histogram
hist(r.student, freq=FALSE, main="Distribution of Studentized Residuals",
xlab="Studentized Residuals", ylab="Density", ylim=c(0,0.5))
# Create range of x-values for normal curve
xfit <- seq(min(r.student)-1, max(r.student)+1, length=40)
# Generate values from the normal distribution at the specified values
yfit <- (dnorm(xfit))
# Add the normal curve
lines(xfit, yfit, ylim=c(0,0.5))
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
plot(lev, ylab = 'Leverage - check')
# Cook's Distance
cd = cooks.distance(model)
plot(cd,ylab="Cooks distances")
abline(4/nrow(train),0)
abline(1,0)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
test.model = function(model, test, type = 'No Model Name Specified', level = 0.95){
pred = predict(model, newdata=test, interval="confidence", level = level)
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(type, " Test MSE: ", test.mse, sep=""))
plot(test[,label.names],pred[,1],xlab = "Actual", ylab = "Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3 ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 +
## x12 + x13 + x14 + x15 + x16 + x17 + x19 + x20 + x21 + x22 +
## x23 + stat1 + stat2 + stat3 + stat4 + stat5 + stat6 + stat7 +
## stat8 + stat9 + stat10 + stat11 + stat12 + stat13 + stat14 +
## stat15 + stat16 + stat17 + stat18 + stat19 + stat20 + stat21 +
## stat22 + stat23 + stat24 + stat25 + stat26 + stat27 + stat28 +
## stat29 + stat30 + stat31 + stat32 + stat33 + stat34 + stat35 +
## stat36 + stat37 + stat38 + stat39 + stat40 + stat41 + stat42 +
## stat43 + stat44 + stat45 + stat46 + stat47 + stat48 + stat49 +
## stat50 + stat51 + stat52 + stat53 + stat54 + stat55 + stat56 +
## stat57 + stat58 + stat59 + stat60 + stat61 + stat62 + stat63 +
## stat64 + stat65 + stat66 + stat67 + stat68 + stat69 + stat70 +
## stat71 + stat72 + stat73 + stat74 + stat75 + stat76 + stat77 +
## stat78 + stat79 + stat80 + stat81 + stat82 + stat83 + stat84 +
## stat85 + stat86 + stat87 + stat88 + stat89 + stat90 + stat91 +
## stat92 + stat93 + stat94 + stat95 + stat96 + stat97 + stat98 +
## stat99 + stat100 + stat101 + stat102 + stat103 + stat104 +
## stat105 + stat106 + stat107 + stat108 + stat109 + stat110 +
## stat111 + stat112 + stat113 + stat114 + stat115 + stat116 +
## stat117 + stat118 + stat119 + stat120 + stat121 + stat122 +
## stat123 + stat124 + stat125 + stat126 + stat127 + stat128 +
## stat129 + stat130 + stat131 + stat132 + stat133 + stat134 +
## stat135 + stat136 + stat137 + stat138 + stat139 + stat140 +
## stat141 + stat142 + stat143 + stat144 + stat145 + stat146 +
## stat147 + stat148 + stat149 + stat150 + stat151 + stat152 +
## stat153 + stat154 + stat155 + stat156 + stat157 + stat158 +
## stat159 + stat160 + stat161 + stat162 + stat163 + stat164 +
## stat165 + stat166 + stat167 + stat168 + stat169 + stat170 +
## stat171 + stat172 + stat173 + stat174 + stat175 + stat176 +
## stat177 + stat178 + stat179 + stat180 + stat181 + stat182 +
## stat183 + stat184 + stat185 + stat186 + stat187 + stat188 +
## stat189 + stat190 + stat191 + stat192 + stat193 + stat194 +
## stat195 + stat196 + stat197 + stat198 + stat199 + stat200 +
## stat201 + stat202 + stat203 + stat204 + stat205 + stat206 +
## stat207 + stat208 + stat209 + stat210 + stat211 + stat212 +
## stat213 + stat214 + stat215 + stat216 + stat217 + sqrt.x18print(grand.mean.formula)## y3 ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full & Grand Means Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.616 -6.101 -1.674 4.446 53.612
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.685e+01 2.775e+00 31.298 < 2e-16 ***
## x1 -1.450e-01 1.901e-01 -0.763 0.445429
## x2 9.691e-02 1.215e-01 0.798 0.425064
## x3 1.076e-02 3.324e-02 0.324 0.746290
## x4 -1.175e-02 2.627e-03 -4.474 7.82e-06 ***
## x5 4.412e-02 8.616e-02 0.512 0.608620
## x6 6.896e-02 1.730e-01 0.399 0.690242
## x7 3.199e+00 1.857e-01 17.233 < 2e-16 ***
## x8 1.254e-01 4.335e-02 2.893 0.003828 **
## x9 9.369e-01 9.680e-02 9.678 < 2e-16 ***
## x10 3.195e-01 8.941e-02 3.574 0.000355 ***
## x11 7.419e+07 2.142e+07 3.463 0.000538 ***
## x12 -6.063e-02 5.455e-02 -1.111 0.266419
## x13 4.699e-02 2.169e-02 2.166 0.030324 *
## x14 -2.461e-01 9.418e-02 -2.614 0.008983 **
## x15 4.396e-02 8.984e-02 0.489 0.624657
## x16 2.865e-01 6.223e-02 4.603 4.25e-06 ***
## x17 4.493e-01 9.460e-02 4.749 2.09e-06 ***
## x19 7.815e-02 4.804e-02 1.627 0.103811
## x20 -3.025e-01 3.343e-01 -0.905 0.365606
## x21 4.269e-02 1.228e-02 3.476 0.000513 ***
## x22 -6.305e-02 1.003e-01 -0.629 0.529592
## x23 3.949e-02 9.551e-02 0.413 0.679277
## stat1 1.147e-02 7.187e-02 0.160 0.873213
## stat2 3.859e-02 7.178e-02 0.538 0.590837
## stat3 1.745e-01 7.211e-02 2.420 0.015560 *
## stat4 -1.582e-01 7.230e-02 -2.189 0.028660 *
## stat5 -4.707e-02 7.266e-02 -0.648 0.517093
## stat6 2.828e-02 7.250e-02 0.390 0.696496
## stat7 -1.895e-02 7.209e-02 -0.263 0.792612
## stat8 6.018e-02 7.229e-02 0.833 0.405144
## stat9 -1.070e-01 7.237e-02 -1.478 0.139478
## stat10 -8.672e-02 7.193e-02 -1.206 0.228022
## stat11 -7.873e-02 7.260e-02 -1.084 0.278201
## stat12 2.245e-02 7.208e-02 0.312 0.755421
## stat13 -1.139e-01 7.157e-02 -1.591 0.111681
## stat14 -2.837e-01 7.143e-02 -3.971 7.23e-05 ***
## stat15 -3.021e-02 7.167e-02 -0.422 0.673336
## stat16 2.735e-02 7.208e-02 0.379 0.704374
## stat17 -3.173e-02 7.144e-02 -0.444 0.656902
## stat18 -8.395e-02 7.192e-02 -1.167 0.243175
## stat19 1.127e-01 7.199e-02 1.566 0.117456
## stat20 -5.161e-02 7.175e-02 -0.719 0.472025
## stat21 -8.546e-02 7.264e-02 -1.177 0.239422
## stat22 -1.122e-01 7.246e-02 -1.549 0.121415
## stat23 1.663e-01 7.155e-02 2.325 0.020129 *
## stat24 -1.400e-01 7.211e-02 -1.941 0.052314 .
## stat25 -1.112e-01 7.193e-02 -1.546 0.122055
## stat26 -1.183e-01 7.194e-02 -1.645 0.100122
## stat27 -3.303e-02 7.224e-02 -0.457 0.647540
## stat28 4.136e-02 7.165e-02 0.577 0.563723
## stat29 2.630e-02 7.254e-02 0.363 0.716938
## stat30 1.579e-02 7.266e-02 0.217 0.827941
## stat31 -8.337e-02 7.270e-02 -1.147 0.251533
## stat32 -7.763e-02 7.237e-02 -1.073 0.283423
## stat33 -1.585e-01 7.191e-02 -2.205 0.027511 *
## stat34 5.484e-02 7.188e-02 0.763 0.445548
## stat35 -9.077e-02 7.236e-02 -1.254 0.209753
## stat36 1.786e-02 7.168e-02 0.249 0.803192
## stat37 -7.202e-02 7.272e-02 -0.990 0.322010
## stat38 9.423e-02 7.223e-02 1.305 0.192093
## stat39 -7.911e-02 7.154e-02 -1.106 0.268873
## stat40 5.435e-03 7.224e-02 0.075 0.940035
## stat41 -1.863e-01 7.151e-02 -2.605 0.009203 **
## stat42 -7.339e-02 7.167e-02 -1.024 0.305910
## stat43 -7.524e-02 7.230e-02 -1.041 0.298091
## stat44 2.353e-02 7.191e-02 0.327 0.743551
## stat45 -5.854e-02 7.222e-02 -0.811 0.417625
## stat46 1.299e-01 7.248e-02 1.793 0.073052 .
## stat47 2.677e-02 7.260e-02 0.369 0.712346
## stat48 9.013e-02 7.225e-02 1.248 0.212248
## stat49 3.311e-02 7.187e-02 0.461 0.644991
## stat50 9.055e-02 7.131e-02 1.270 0.204174
## stat51 8.292e-02 7.229e-02 1.147 0.251405
## stat52 4.620e-02 7.248e-02 0.637 0.523910
## stat53 -8.136e-02 7.292e-02 -1.116 0.264599
## stat54 -7.744e-02 7.255e-02 -1.067 0.285828
## stat55 1.078e-01 7.167e-02 1.504 0.132666
## stat56 -2.808e-02 7.230e-02 -0.388 0.697810
## stat57 5.821e-02 7.144e-02 0.815 0.415215
## stat58 2.011e-02 7.152e-02 0.281 0.778625
## stat59 5.899e-02 7.217e-02 0.817 0.413702
## stat60 1.700e-01 7.222e-02 2.353 0.018644 *
## stat61 -7.435e-02 7.226e-02 -1.029 0.303521
## stat62 -1.737e-03 7.197e-02 -0.024 0.980744
## stat63 8.262e-03 7.225e-02 0.114 0.908958
## stat64 -8.245e-02 7.178e-02 -1.149 0.250764
## stat65 -7.062e-02 7.218e-02 -0.978 0.327885
## stat66 3.177e-02 7.265e-02 0.437 0.661840
## stat67 -5.352e-02 7.254e-02 -0.738 0.460648
## stat68 -3.099e-03 7.226e-02 -0.043 0.965794
## stat69 1.180e-02 7.219e-02 0.163 0.870146
## stat70 4.033e-02 7.165e-02 0.563 0.573562
## stat71 4.958e-02 7.189e-02 0.690 0.490427
## stat72 9.083e-02 7.299e-02 1.244 0.213396
## stat73 1.116e-01 7.283e-02 1.533 0.125373
## stat74 -1.243e-02 7.244e-02 -0.172 0.863789
## stat75 -6.499e-02 7.250e-02 -0.896 0.370040
## stat76 1.170e-01 7.243e-02 1.616 0.106189
## stat77 -4.972e-02 7.228e-02 -0.688 0.491494
## stat78 -1.436e-02 7.221e-02 -0.199 0.842412
## stat79 -1.580e-02 7.219e-02 -0.219 0.826767
## stat80 -7.193e-03 7.216e-02 -0.100 0.920596
## stat81 7.973e-02 7.217e-02 1.105 0.269355
## stat82 6.707e-02 7.187e-02 0.933 0.350787
## stat83 -5.133e-02 7.213e-02 -0.712 0.476735
## stat84 -1.032e-01 7.252e-02 -1.423 0.154761
## stat85 -4.563e-02 7.170e-02 -0.636 0.524532
## stat86 -8.050e-03 7.211e-02 -0.112 0.911117
## stat87 -9.259e-02 7.219e-02 -1.283 0.199682
## stat88 -6.432e-02 7.169e-02 -0.897 0.369694
## stat89 -7.823e-02 7.165e-02 -1.092 0.274906
## stat90 -7.884e-02 7.225e-02 -1.091 0.275241
## stat91 -7.849e-02 7.177e-02 -1.094 0.274155
## stat92 -1.271e-01 7.236e-02 -1.756 0.079093 .
## stat93 -5.421e-02 7.322e-02 -0.740 0.459128
## stat94 -4.610e-02 7.215e-02 -0.639 0.522894
## stat95 -1.083e-02 7.180e-02 -0.151 0.880070
## stat96 -9.717e-03 7.179e-02 -0.135 0.892327
## stat97 9.013e-03 7.144e-02 0.126 0.899602
## stat98 1.064e+00 7.069e-02 15.046 < 2e-16 ***
## stat99 6.877e-02 7.291e-02 0.943 0.345662
## stat100 1.760e-01 7.221e-02 2.437 0.014836 *
## stat101 -8.847e-02 7.322e-02 -1.208 0.226953
## stat102 -1.668e-02 7.178e-02 -0.232 0.816240
## stat103 -4.988e-02 7.315e-02 -0.682 0.495343
## stat104 -8.342e-02 7.186e-02 -1.161 0.245713
## stat105 1.096e-01 7.183e-02 1.525 0.127208
## stat106 -4.630e-02 7.198e-02 -0.643 0.520098
## stat107 -2.564e-02 7.236e-02 -0.354 0.723082
## stat108 -6.249e-02 7.216e-02 -0.866 0.386495
## stat109 -1.623e-02 7.161e-02 -0.227 0.820736
## stat110 -9.649e-01 7.162e-02 -13.473 < 2e-16 ***
## stat111 2.862e-02 7.203e-02 0.397 0.691090
## stat112 -3.696e-02 7.254e-02 -0.509 0.610472
## stat113 -4.231e-02 7.246e-02 -0.584 0.559303
## stat114 1.209e-02 7.197e-02 0.168 0.866548
## stat115 2.107e-02 7.208e-02 0.292 0.770064
## stat116 4.963e-02 7.250e-02 0.684 0.493718
## stat117 8.677e-02 7.236e-02 1.199 0.230519
## stat118 -2.435e-02 7.184e-02 -0.339 0.734644
## stat119 -1.645e-02 7.238e-02 -0.227 0.820259
## stat120 7.426e-03 7.129e-02 0.104 0.917044
## stat121 7.223e-02 7.207e-02 1.002 0.316306
## stat122 4.204e-03 7.189e-02 0.058 0.953368
## stat123 -4.135e-02 7.349e-02 -0.563 0.573686
## stat124 -3.512e-03 7.182e-02 -0.049 0.961005
## stat125 2.895e-02 7.210e-02 0.402 0.688038
## stat126 1.161e-01 7.191e-02 1.614 0.106608
## stat127 2.731e-02 7.182e-02 0.380 0.703754
## stat128 -7.463e-02 7.172e-02 -1.041 0.298136
## stat129 2.372e-02 7.175e-02 0.331 0.740961
## stat130 7.141e-02 7.226e-02 0.988 0.323093
## stat131 7.253e-02 7.223e-02 1.004 0.315344
## stat132 2.901e-02 7.169e-02 0.405 0.685749
## stat133 6.596e-02 7.212e-02 0.915 0.360452
## stat134 -1.121e-02 7.165e-02 -0.156 0.875705
## stat135 -1.084e-01 7.210e-02 -1.503 0.132817
## stat136 3.287e-02 7.232e-02 0.455 0.649453
## stat137 -2.883e-02 7.132e-02 -0.404 0.686075
## stat138 4.917e-02 7.191e-02 0.684 0.494176
## stat139 1.311e-02 7.211e-02 0.182 0.855743
## stat140 3.102e-03 7.192e-02 0.043 0.965601
## stat141 1.493e-02 7.154e-02 0.209 0.834695
## stat142 -4.544e-02 7.297e-02 -0.623 0.533445
## stat143 4.106e-02 7.201e-02 0.570 0.568572
## stat144 1.541e-01 7.182e-02 2.146 0.031929 *
## stat145 -2.817e-02 7.289e-02 -0.386 0.699195
## stat146 -1.272e-01 7.234e-02 -1.758 0.078763 .
## stat147 -4.878e-02 7.304e-02 -0.668 0.504262
## stat148 -1.102e-01 7.158e-02 -1.539 0.123919
## stat149 -1.461e-01 7.266e-02 -2.010 0.044439 *
## stat150 1.951e-02 7.219e-02 0.270 0.787013
## stat151 -1.533e-01 7.296e-02 -2.102 0.035640 *
## stat152 -1.658e-02 7.195e-02 -0.230 0.817775
## stat153 4.535e-02 7.313e-02 0.620 0.535173
## stat154 -3.718e-02 7.282e-02 -0.511 0.609642
## stat155 -4.734e-02 7.210e-02 -0.657 0.511429
## stat156 1.071e-01 7.261e-02 1.475 0.140315
## stat157 -3.438e-02 7.151e-02 -0.481 0.630650
## stat158 -5.408e-02 7.278e-02 -0.743 0.457488
## stat159 -2.453e-02 7.154e-02 -0.343 0.731663
## stat160 7.111e-02 7.202e-02 0.987 0.323492
## stat161 6.475e-02 7.269e-02 0.891 0.373065
## stat162 -6.369e-02 7.142e-02 -0.892 0.372580
## stat163 -3.999e-03 7.271e-02 -0.055 0.956141
## stat164 5.963e-02 7.245e-02 0.823 0.410472
## stat165 4.134e-02 7.196e-02 0.574 0.565694
## stat166 -7.318e-02 7.149e-02 -1.024 0.306039
## stat167 -3.924e-02 7.207e-02 -0.544 0.586122
## stat168 -1.870e-02 7.169e-02 -0.261 0.794189
## stat169 9.179e-03 7.226e-02 0.127 0.898924
## stat170 -3.458e-02 7.212e-02 -0.480 0.631585
## stat171 9.385e-03 7.241e-02 0.130 0.896872
## stat172 6.797e-02 7.208e-02 0.943 0.345725
## stat173 -6.109e-02 7.259e-02 -0.842 0.400049
## stat174 2.614e-02 7.211e-02 0.362 0.717015
## stat175 -1.419e-01 7.257e-02 -1.955 0.050574 .
## stat176 8.135e-02 7.159e-02 1.136 0.255869
## stat177 -4.616e-03 7.267e-02 -0.064 0.949359
## stat178 -3.525e-02 7.272e-02 -0.485 0.627840
## stat179 -1.135e-02 7.193e-02 -0.158 0.874647
## stat180 -3.897e-02 7.170e-02 -0.544 0.586762
## stat181 1.379e-02 7.241e-02 0.190 0.849021
## stat182 5.762e-02 7.249e-02 0.795 0.426723
## stat183 6.241e-02 7.164e-02 0.871 0.383680
## stat184 -5.415e-03 7.252e-02 -0.075 0.940481
## stat185 -2.540e-03 7.172e-02 -0.035 0.971745
## stat186 -8.810e-02 7.283e-02 -1.210 0.226438
## stat187 -8.976e-02 7.204e-02 -1.246 0.212834
## stat188 2.709e-02 7.199e-02 0.376 0.706690
## stat189 7.004e-02 7.220e-02 0.970 0.332022
## stat190 4.979e-02 7.192e-02 0.692 0.488760
## stat191 -1.685e-02 7.245e-02 -0.233 0.816106
## stat192 8.263e-03 7.335e-02 0.113 0.910306
## stat193 -1.471e-02 7.291e-02 -0.202 0.840153
## stat194 -1.114e-02 7.206e-02 -0.155 0.877152
## stat195 7.394e-02 7.251e-02 1.020 0.307927
## stat196 -3.392e-02 7.305e-02 -0.464 0.642405
## stat197 -2.234e-02 7.159e-02 -0.312 0.755051
## stat198 -4.684e-02 7.226e-02 -0.648 0.516822
## stat199 8.525e-02 7.168e-02 1.189 0.234366
## stat200 -1.416e-01 7.115e-02 -1.990 0.046677 *
## stat201 7.595e-03 7.221e-02 0.105 0.916244
## stat202 -6.450e-02 7.275e-02 -0.887 0.375340
## stat203 -3.555e-03 7.197e-02 -0.049 0.960605
## stat204 -6.539e-02 7.158e-02 -0.914 0.361004
## stat205 -1.239e-01 7.147e-02 -1.733 0.083177 .
## stat206 -1.175e-02 7.216e-02 -0.163 0.870626
## stat207 7.698e-02 7.217e-02 1.067 0.286175
## stat208 -1.556e-02 7.244e-02 -0.215 0.829943
## stat209 1.115e-02 7.189e-02 0.155 0.876725
## stat210 -4.343e-02 7.258e-02 -0.598 0.549659
## stat211 -1.804e-02 7.196e-02 -0.251 0.802106
## stat212 1.014e-03 7.206e-02 0.014 0.988770
## stat213 -6.849e-02 7.272e-02 -0.942 0.346333
## stat214 -9.589e-02 7.194e-02 -1.333 0.182590
## stat215 -3.625e-02 7.200e-02 -0.503 0.614713
## stat216 -7.945e-02 7.195e-02 -1.104 0.269500
## stat217 9.684e-02 7.207e-02 1.344 0.179110
## sqrt.x18 7.352e+00 2.745e-01 26.786 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.483 on 5761 degrees of freedom
## Multiple R-squared: 0.249, Adjusted R-squared: 0.2177
## F-statistic: 7.958 on 240 and 5761 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model.full, data.train)
## [1] "Number of data points that have Cook's D > 4/n: 294"
## [1] "Number of data points that have Cook's D > 1: 0"Just trial removing all high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.3966 -5.0261 -0.9066 4.6154 21.1658
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.402e+01 2.203e+00 38.133 < 2e-16 ***
## x1 -8.027e-02 1.510e-01 -0.531 0.595159
## x2 7.001e-02 9.633e-02 0.727 0.467432
## x3 1.073e-02 2.634e-02 0.407 0.683849
## x4 -1.362e-02 2.081e-03 -6.542 6.61e-11 ***
## x5 1.021e-01 6.835e-02 1.494 0.135336
## x6 -3.398e-02 1.369e-01 -0.248 0.803918
## x7 3.183e+00 1.471e-01 21.632 < 2e-16 ***
## x8 1.327e-01 3.439e-02 3.859 0.000115 ***
## x9 8.506e-01 7.668e-02 11.092 < 2e-16 ***
## x10 4.104e-01 7.100e-02 5.780 7.87e-09 ***
## x11 8.265e+07 1.700e+07 4.862 1.19e-06 ***
## x12 -4.358e-03 4.316e-02 -0.101 0.919574
## x13 5.950e-02 1.722e-02 3.456 0.000553 ***
## x14 -1.030e-01 7.469e-02 -1.379 0.167924
## x15 1.135e-02 7.121e-02 0.159 0.873391
## x16 2.977e-01 4.931e-02 6.038 1.67e-09 ***
## x17 4.305e-01 7.502e-02 5.739 1.00e-08 ***
## x19 8.173e-02 3.814e-02 2.143 0.032187 *
## x20 -2.108e-01 2.651e-01 -0.795 0.426610
## x21 4.273e-02 9.747e-03 4.383 1.19e-05 ***
## x22 -9.985e-02 7.944e-02 -1.257 0.208841
## x23 9.483e-02 7.580e-02 1.251 0.210951
## stat1 6.923e-03 5.694e-02 0.122 0.903228
## stat2 3.740e-02 5.689e-02 0.657 0.510929
## stat3 2.058e-01 5.722e-02 3.597 0.000325 ***
## stat4 -1.759e-01 5.748e-02 -3.061 0.002218 **
## stat5 -4.251e-02 5.766e-02 -0.737 0.460966
## stat6 -4.786e-02 5.751e-02 -0.832 0.405363
## stat7 -4.005e-02 5.702e-02 -0.702 0.482453
## stat8 3.697e-02 5.725e-02 0.646 0.518479
## stat9 -8.281e-02 5.739e-02 -1.443 0.149130
## stat10 -7.395e-02 5.690e-02 -1.300 0.193787
## stat11 -1.326e-01 5.748e-02 -2.308 0.021059 *
## stat12 2.640e-02 5.709e-02 0.462 0.643770
## stat13 -1.186e-01 5.670e-02 -2.091 0.036597 *
## stat14 -2.969e-01 5.659e-02 -5.246 1.61e-07 ***
## stat15 -1.258e-01 5.686e-02 -2.213 0.026927 *
## stat16 -1.606e-02 5.702e-02 -0.282 0.778198
## stat17 -2.239e-02 5.666e-02 -0.395 0.692709
## stat18 -5.086e-02 5.690e-02 -0.894 0.371452
## stat19 7.363e-02 5.729e-02 1.285 0.198757
## stat20 3.570e-02 5.696e-02 0.627 0.530811
## stat21 -8.643e-02 5.758e-02 -1.501 0.133406
## stat22 -6.810e-02 5.734e-02 -1.188 0.235004
## stat23 2.093e-01 5.687e-02 3.681 0.000234 ***
## stat24 -1.335e-01 5.724e-02 -2.332 0.019717 *
## stat25 -6.510e-02 5.699e-02 -1.142 0.253366
## stat26 -1.006e-01 5.709e-02 -1.762 0.078054 .
## stat27 -6.127e-02 5.731e-02 -1.069 0.284998
## stat28 -2.093e-02 5.686e-02 -0.368 0.712788
## stat29 -2.241e-02 5.747e-02 -0.390 0.696598
## stat30 3.946e-03 5.744e-02 0.069 0.945224
## stat31 -4.145e-02 5.750e-02 -0.721 0.471001
## stat32 -8.462e-02 5.746e-02 -1.473 0.140886
## stat33 -1.333e-01 5.707e-02 -2.336 0.019552 *
## stat34 8.642e-02 5.699e-02 1.517 0.129449
## stat35 -1.398e-01 5.742e-02 -2.434 0.014970 *
## stat36 -2.093e-02 5.691e-02 -0.368 0.713028
## stat37 -9.646e-03 5.775e-02 -0.167 0.867351
## stat38 1.204e-01 5.719e-02 2.105 0.035297 *
## stat39 -8.562e-02 5.665e-02 -1.511 0.130746
## stat40 -3.005e-03 5.736e-02 -0.052 0.958230
## stat41 -1.988e-01 5.658e-02 -3.514 0.000445 ***
## stat42 -5.194e-02 5.695e-02 -0.912 0.361764
## stat43 -7.610e-02 5.743e-02 -1.325 0.185226
## stat44 4.100e-02 5.705e-02 0.719 0.472401
## stat45 -6.098e-02 5.731e-02 -1.064 0.287341
## stat46 6.351e-02 5.751e-02 1.104 0.269480
## stat47 3.533e-02 5.759e-02 0.614 0.539525
## stat48 2.040e-02 5.712e-02 0.357 0.720979
## stat49 -3.507e-02 5.701e-02 -0.615 0.538524
## stat50 9.173e-02 5.659e-02 1.621 0.105073
## stat51 3.025e-02 5.731e-02 0.528 0.597666
## stat52 7.190e-02 5.750e-02 1.250 0.211174
## stat53 -5.482e-02 5.774e-02 -0.949 0.342440
## stat54 -7.750e-02 5.767e-02 -1.344 0.179089
## stat55 8.676e-02 5.684e-02 1.526 0.126992
## stat56 9.326e-03 5.732e-02 0.163 0.870752
## stat57 2.484e-02 5.680e-02 0.437 0.661831
## stat58 2.732e-02 5.659e-02 0.483 0.629269
## stat59 7.988e-02 5.710e-02 1.399 0.161910
## stat60 2.283e-01 5.728e-02 3.986 6.81e-05 ***
## stat61 -1.258e-01 5.727e-02 -2.196 0.028121 *
## stat62 -4.339e-02 5.694e-02 -0.762 0.446085
## stat63 1.375e-02 5.734e-02 0.240 0.810455
## stat64 4.533e-03 5.693e-02 0.080 0.936533
## stat65 -2.502e-02 5.720e-02 -0.437 0.661778
## stat66 3.392e-02 5.757e-02 0.589 0.555842
## stat67 4.196e-02 5.743e-02 0.731 0.465034
## stat68 -2.113e-02 5.711e-02 -0.370 0.711357
## stat69 -2.029e-02 5.720e-02 -0.355 0.722783
## stat70 4.847e-02 5.682e-02 0.853 0.393682
## stat71 8.025e-02 5.716e-02 1.404 0.160370
## stat72 6.316e-02 5.784e-02 1.092 0.274867
## stat73 9.387e-02 5.785e-02 1.623 0.104751
## stat74 2.178e-02 5.748e-02 0.379 0.704799
## stat75 -5.051e-03 5.743e-02 -0.088 0.929922
## stat76 8.991e-02 5.733e-02 1.568 0.116888
## stat77 5.153e-03 5.729e-02 0.090 0.928337
## stat78 -5.851e-02 5.710e-02 -1.025 0.305591
## stat79 9.293e-02 5.710e-02 1.627 0.103695
## stat80 6.450e-03 5.714e-02 0.113 0.910140
## stat81 5.144e-02 5.720e-02 0.899 0.368559
## stat82 4.058e-03 5.696e-02 0.071 0.943206
## stat83 -4.462e-02 5.705e-02 -0.782 0.434171
## stat84 -1.226e-01 5.745e-02 -2.134 0.032912 *
## stat85 -1.281e-01 5.686e-02 -2.252 0.024349 *
## stat86 2.842e-02 5.719e-02 0.497 0.619182
## stat87 -9.555e-02 5.716e-02 -1.672 0.094621 .
## stat88 6.486e-03 5.691e-02 0.114 0.909260
## stat89 -2.404e-02 5.692e-02 -0.422 0.672746
## stat90 -1.231e-01 5.733e-02 -2.147 0.031798 *
## stat91 -4.420e-02 5.674e-02 -0.779 0.436050
## stat92 -1.054e-01 5.736e-02 -1.838 0.066153 .
## stat93 1.442e-02 5.819e-02 0.248 0.804350
## stat94 2.169e-02 5.703e-02 0.380 0.703694
## stat95 2.463e-02 5.696e-02 0.432 0.665528
## stat96 -2.507e-02 5.704e-02 -0.439 0.660329
## stat97 1.865e-02 5.660e-02 0.330 0.741753
## stat98 9.468e-01 5.597e-02 16.917 < 2e-16 ***
## stat99 1.062e-01 5.780e-02 1.837 0.066300 .
## stat100 1.872e-01 5.733e-02 3.265 0.001103 **
## stat101 -6.744e-02 5.811e-02 -1.160 0.245932
## stat102 -1.487e-03 5.684e-02 -0.026 0.979130
## stat103 -7.084e-02 5.783e-02 -1.225 0.220697
## stat104 -4.217e-02 5.700e-02 -0.740 0.459400
## stat105 1.169e-01 5.698e-02 2.051 0.040302 *
## stat106 -4.959e-02 5.699e-02 -0.870 0.384265
## stat107 1.315e-02 5.740e-02 0.229 0.818745
## stat108 -2.942e-02 5.727e-02 -0.514 0.607469
## stat109 -3.762e-02 5.682e-02 -0.662 0.507959
## stat110 -8.967e-01 5.666e-02 -15.826 < 2e-16 ***
## stat111 2.758e-02 5.702e-02 0.484 0.628649
## stat112 -3.112e-02 5.759e-02 -0.540 0.589003
## stat113 -1.426e-03 5.736e-02 -0.025 0.980170
## stat114 3.470e-02 5.713e-02 0.607 0.543660
## stat115 7.429e-02 5.722e-02 1.298 0.194239
## stat116 2.384e-02 5.744e-02 0.415 0.678142
## stat117 5.650e-02 5.719e-02 0.988 0.323183
## stat118 2.903e-02 5.693e-02 0.510 0.610113
## stat119 4.064e-02 5.725e-02 0.710 0.477805
## stat120 -5.773e-02 5.643e-02 -1.023 0.306325
## stat121 3.670e-02 5.703e-02 0.644 0.519862
## stat122 -6.160e-02 5.705e-02 -1.080 0.280355
## stat123 -1.627e-03 5.810e-02 -0.028 0.977662
## stat124 -1.176e-02 5.694e-02 -0.207 0.836359
## stat125 9.877e-03 5.716e-02 0.173 0.862825
## stat126 1.036e-01 5.706e-02 1.816 0.069381 .
## stat127 -4.994e-02 5.695e-02 -0.877 0.380618
## stat128 -1.548e-01 5.674e-02 -2.728 0.006387 **
## stat129 1.248e-02 5.680e-02 0.220 0.826044
## stat130 6.341e-02 5.725e-02 1.108 0.268101
## stat131 4.252e-02 5.720e-02 0.743 0.457256
## stat132 2.991e-02 5.685e-02 0.526 0.598868
## stat133 7.470e-02 5.730e-02 1.304 0.192421
## stat134 1.613e-02 5.675e-02 0.284 0.776225
## stat135 -1.140e-01 5.717e-02 -1.995 0.046115 *
## stat136 1.877e-02 5.727e-02 0.328 0.743057
## stat137 1.786e-02 5.637e-02 0.317 0.751445
## stat138 2.182e-02 5.698e-02 0.383 0.701843
## stat139 1.796e-02 5.723e-02 0.314 0.753659
## stat140 1.155e-02 5.687e-02 0.203 0.839089
## stat141 7.075e-02 5.676e-02 1.247 0.212607
## stat142 1.208e-02 5.787e-02 0.209 0.834683
## stat143 7.083e-03 5.710e-02 0.124 0.901293
## stat144 1.599e-01 5.687e-02 2.812 0.004937 **
## stat145 -7.801e-02 5.782e-02 -1.349 0.177358
## stat146 -1.864e-01 5.731e-02 -3.253 0.001151 **
## stat147 -6.048e-02 5.794e-02 -1.044 0.296603
## stat148 -7.885e-02 5.682e-02 -1.388 0.165337
## stat149 -1.741e-01 5.770e-02 -3.017 0.002563 **
## stat150 -2.127e-04 5.738e-02 -0.004 0.997042
## stat151 -1.543e-02 5.792e-02 -0.266 0.789895
## stat152 2.596e-02 5.701e-02 0.455 0.648915
## stat153 8.343e-02 5.793e-02 1.440 0.149879
## stat154 -7.774e-03 5.772e-02 -0.135 0.892875
## stat155 -1.463e-02 5.719e-02 -0.256 0.798088
## stat156 8.694e-02 5.748e-02 1.513 0.130447
## stat157 -3.131e-02 5.669e-02 -0.552 0.580798
## stat158 -4.111e-03 5.769e-02 -0.071 0.943184
## stat159 9.523e-03 5.671e-02 0.168 0.866638
## stat160 6.432e-02 5.722e-02 1.124 0.261074
## stat161 1.801e-02 5.752e-02 0.313 0.754266
## stat162 -9.042e-02 5.651e-02 -1.600 0.109640
## stat163 4.708e-02 5.782e-02 0.814 0.415527
## stat164 2.489e-02 5.755e-02 0.433 0.665393
## stat165 6.987e-02 5.718e-02 1.222 0.221824
## stat166 -7.134e-02 5.659e-02 -1.261 0.207525
## stat167 -6.640e-02 5.702e-02 -1.164 0.244288
## stat168 -2.001e-02 5.671e-02 -0.353 0.724248
## stat169 -1.182e-02 5.749e-02 -0.206 0.837130
## stat170 -4.668e-03 5.731e-02 -0.081 0.935087
## stat171 -3.719e-02 5.745e-02 -0.647 0.517387
## stat172 1.502e-01 5.705e-02 2.633 0.008496 **
## stat173 -2.598e-03 5.757e-02 -0.045 0.964008
## stat174 9.298e-02 5.714e-02 1.627 0.103770
## stat175 -1.147e-01 5.750e-02 -1.994 0.046149 *
## stat176 -2.386e-02 5.674e-02 -0.420 0.674188
## stat177 -8.789e-02 5.758e-02 -1.526 0.126952
## stat178 -1.121e-03 5.762e-02 -0.019 0.984478
## stat179 -1.125e-04 5.691e-02 -0.002 0.998423
## stat180 -3.427e-03 5.694e-02 -0.060 0.952006
## stat181 6.143e-02 5.717e-02 1.074 0.282648
## stat182 9.044e-02 5.757e-02 1.571 0.116240
## stat183 4.358e-02 5.695e-02 0.765 0.444126
## stat184 3.612e-03 5.755e-02 0.063 0.949969
## stat185 1.065e-02 5.679e-02 0.187 0.851307
## stat186 2.604e-02 5.783e-02 0.450 0.652564
## stat187 -5.582e-02 5.701e-02 -0.979 0.327579
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## stat195 -2.277e-02 5.757e-02 -0.396 0.692429
## stat196 -6.405e-02 5.787e-02 -1.107 0.268482
## stat197 -6.444e-02 5.672e-02 -1.136 0.255983
## stat198 -2.276e-02 5.724e-02 -0.398 0.690869
## stat199 5.630e-02 5.686e-02 0.990 0.322128
## stat200 -7.753e-02 5.641e-02 -1.374 0.169344
## stat201 6.240e-02 5.739e-02 1.087 0.276991
## stat202 4.789e-03 5.776e-02 0.083 0.933920
## stat203 3.387e-02 5.694e-02 0.595 0.551996
## stat204 -3.442e-02 5.681e-02 -0.606 0.544659
## stat205 1.867e-03 5.644e-02 0.033 0.973619
## stat206 -7.531e-02 5.710e-02 -1.319 0.187234
## stat207 1.163e-01 5.729e-02 2.030 0.042385 *
## stat208 4.964e-02 5.749e-02 0.863 0.387940
## stat209 -3.018e-02 5.698e-02 -0.530 0.596345
## stat210 -9.023e-02 5.753e-02 -1.569 0.116806
## stat211 -6.011e-02 5.717e-02 -1.051 0.293127
## stat212 3.264e-02 5.716e-02 0.571 0.568037
## stat213 -5.487e-02 5.757e-02 -0.953 0.340543
## stat214 -1.571e-02 5.705e-02 -0.275 0.783063
## stat215 -1.050e-02 5.710e-02 -0.184 0.854158
## stat216 -7.282e-02 5.690e-02 -1.280 0.200719
## stat217 6.858e-02 5.715e-02 1.200 0.230206
## sqrt.x18 7.104e+00 2.166e-01 32.797 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.322 on 5467 degrees of freedom
## Multiple R-squared: 0.345, Adjusted R-squared: 0.3162
## F-statistic: 12 on 240 and 5467 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 313"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# See if you can check the distribution (boxplots) of the high leverage points and the other pointsmodel.null = lm(grand.mean.formula, data.train)
summary(model.null)##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.475 -7.111 -1.418 5.765 57.048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 125.3874 0.1384 906.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.72 on 6001 degrees of freedomplot.diagnostics(model.null, data.train)
## hat values (leverages) are all = 0.0001666111
## and there are no factor predictors; no plot no. 5
## Warning in plot.window(...): relative range of values = 32 * EPS, is small
## (axis 2)
## [1] "Number of data points that have Cook's D > 4/n: 288"
## [1] "Number of data points that have Cook's D > 1: 0"## 3167 2628 2824 3867 6081
## 2.766968e-04 6.075751e-04 1.752800e-05 1.420833e-03 6.526420e-06
## 3220 4244 8540 1169 2211
## 6.272686e-05 4.230348e-04 1.429094e-05 8.588340e-06 1.067298e-05
## 6546 4289 1976 8380 2866
## 2.807454e-05 1.831550e-04 1.506575e-05 3.787546e-06 6.494500e-05
## 3788 8053 9864 416 9047
## 7.224316e-04 2.419123e-04 8.234212e-05 1.787319e-04 1.550165e-04
## 9999 5828 295 6445 2207
## 6.988131e-04 1.898714e-06 4.563399e-07 1.366178e-03 1.914186e-03
## 7690 9633 4140 663 3196
## 1.851851e-04 2.888545e-04 4.802821e-05 4.518087e-07 9.375271e-05
## 2840 7120 90 4490 6380
## 1.898486e-04 1.417958e-05 3.989482e-05 4.516913e-05 1.376145e-05
## 967 3004 1799 3419 3587
## 4.968134e-05 2.142821e-05 8.099256e-05 7.927365e-08 3.932224e-05
## 5428 239 5688 7541 2251
## 6.711402e-05 1.316702e-04 4.716176e-05 1.160898e-04 2.325306e-05
## 3825 2835 7938 8698 7260
## 3.502886e-04 5.293986e-07 6.723090e-05 3.581464e-04 3.744974e-06
## 6975 6994 6857 7142 1894
## 7.485017e-05 6.646784e-06 1.055727e-04 4.962125e-05 1.174059e-03
## 194 380 8328 6204 139
## 8.281760e-06 2.716333e-06 2.401745e-04 1.633627e-04 2.219861e-04
## 2906 7989 9096 1831 7750
## 1.969344e-04 2.879622e-05 1.837915e-06 1.091072e-04 2.544308e-06
## 3234 8613 6837 4075 9425
## 5.385971e-04 1.511735e-04 4.230136e-05 7.550008e-06 4.627807e-04
## 8638 6781 7776 6574 5504
## 8.903560e-07 1.818659e-04 6.082949e-05 2.103581e-04 2.138838e-05
## 2176 8304 6554 584 5371
## 1.660370e-05 4.563565e-06 1.077894e-05 8.221658e-05 1.120124e-03
## 8509 9291 1015 8768 2002
## 3.123289e-06 4.289249e-04 3.759614e-03 1.349060e-04 8.218300e-05
## 5639 7835 8466 7308 203
## 4.738501e-04 4.269886e-06 3.968390e-05 2.385441e-05 6.500769e-05
## 7861 5452 6130 9697 4380
## 4.098414e-06 2.442987e-04 3.257722e-05 4.023593e-04 6.648707e-04
## 2068 8978 8209 3410 5215
## 7.318584e-05 2.330067e-05 6.708983e-05 1.274697e-06 2.094846e-06
## 2420 6525 8052 9686 4308
## 3.891689e-04 3.199670e-05 6.509774e-06 2.625818e-04 3.340661e-07
## 8757 6043 4787 3622 2244
## 9.558891e-06 2.216363e-04 1.115245e-04 1.279303e-05 5.553771e-06
## 4837 5522 3061 526 3786
## 1.483131e-04 2.680462e-05 1.189356e-05 2.660867e-04 6.452981e-05
## 6217 4098 212 9630 3005
## 2.830533e-04 1.697948e-04 1.181216e-04 1.584876e-04 2.741402e-05
## 187 6293 4454 2505 14
## 2.047225e-05 3.524712e-04 3.333449e-05 1.565678e-06 1.173125e-05
## 371 4034 2596 7397 7538
## 2.466190e-04 2.704488e-04 2.425059e-05 1.903970e-04 9.136198e-05
## 1008 343 7313 2953 241
## 4.714950e-04 1.092714e-03 3.400492e-04 4.605558e-06 3.289767e-06
## 8008 9602 3152 8950 3087
## 2.564568e-04 1.813676e-05 1.407687e-08 1.859513e-05 9.914654e-05
## 9676 7848 5327 5763 4192
## 9.216358e-05 1.982943e-05 5.529417e-05 3.805756e-05 2.720011e-04
## 5339 6898 540 8763 9340
## 8.314713e-05 1.815243e-03 1.645205e-04 5.287024e-05 1.859508e-05
## 3074 1134 8708 1589 6084
## 1.023458e-05 7.411629e-05 1.442302e-04 2.438302e-04 4.531082e-06
## 6545 1942 5446 3247 7894
## 3.725938e-04 1.109797e-05 4.401416e-04 6.231259e-04 8.816285e-07
## 3927 4207 3182 9715 9967
## 4.896905e-05 2.911860e-06 5.190506e-05 6.346447e-04 2.056013e-05
## 1294 4100 9817 3655 5413
## 5.524670e-04 2.036042e-04 2.542384e-04 1.084125e-04 6.925690e-04
## 3266 82 9971 5051 8998
## 2.278037e-04 2.521548e-05 1.319757e-04 1.441672e-04 6.590720e-05
## 2630 3224 4129 2719 174
## 1.541882e-05 3.149339e-04 3.416835e-04 6.781526e-06 5.901212e-04
## 3157 4819 9305 3277 2934
## 1.645252e-05 2.649582e-05 1.236130e-04 3.059425e-04 5.508135e-05
## 8444 6684 5770 4435 236
## 1.607276e-04 7.891395e-05 1.016927e-04 3.808692e-04 1.617149e-04
## 6653 8217 2115 9091 91
## 9.000036e-05 2.822148e-05 1.176107e-04 8.115263e-05 5.728443e-06
## 3233 7729 7886 1300 1652
## 2.596428e-04 9.480635e-05 1.885576e-05 4.410587e-07 1.884735e-06
## 4021 3370 4134 3223 5997
## 8.558135e-05 1.693246e-04 2.147292e-05 3.812672e-05 3.091550e-06
## 581 2999 7105 900 3297
## 1.603670e-06 4.765714e-05 4.424617e-05 4.929250e-04 9.097682e-06
## 4812 8673 3590 3608 704
## 5.545014e-04 5.253449e-04 9.685688e-05 1.822791e-05 3.466979e-04
## 6408 4565 3390 9420 9237
## 6.986565e-04 1.138745e-04 1.079480e-04 7.691498e-05 4.861885e-05
## 6320 2497 8697 625 1850
## 6.751408e-04 1.208127e-04 3.916120e-05 2.155656e-04 8.937283e-06
## 1277 7669 1322 5547 2708
## 5.934206e-04 6.154492e-06 1.246768e-04 5.987517e-05 1.604400e-05
## 2169 3434 1674 1752 7337
## 1.669039e-06 5.445608e-04 2.689397e-04 5.900723e-07 2.698004e-05
## 5067 9326 1014 9208 8997
## 5.450977e-05 3.513242e-04 1.143281e-04 1.778436e-04 1.775451e-04
## 1477 3586 1594 3685 6252
## 1.084970e-03 6.788091e-06 1.368624e-04 1.100579e-05 9.239413e-05
## 7787 2798 5462 1877 6101
## 6.078699e-05 3.694628e-06 6.647883e-05 1.071869e-07 5.056363e-04
## 6175 9087 1067 1524 2908
## 9.749990e-06 6.226974e-06 8.045072e-05 1.436760e-06 1.019852e-04
## 7909 6373 4221 1767 5125
## 1.347693e-03 3.626183e-05 5.247598e-05 8.206428e-05 3.386400e-06
## 9215 5664 5274 3130 8855
## 5.217648e-05 5.881024e-04 1.212927e-05 1.259591e-04 2.106741e-04
## 9765 8424 4886 2857 4239
## 3.234798e-06 3.427250e-06 2.129705e-05 1.310146e-05 2.112833e-06
## 6387 9932 1900 7956 7930
## 1.096877e-05 3.028943e-04 3.832405e-04 2.725721e-05 2.015069e-05
## 1451 4883 5894 9995 9478
## 5.920975e-07 5.598439e-06 1.653003e-05 1.241725e-04 5.510618e-05
## 4150 8404 6357 9354 5086
## 7.481411e-05 3.856726e-04 2.029964e-05 8.914536e-05 9.246313e-05
## 1622 370 6940 7888 679
## 1.387952e-03 1.486051e-03 4.819378e-04 3.246234e-04 2.339714e-04
## 1922 1794 5092 1579 7449
## 6.497271e-05 1.797742e-04 7.647642e-05 6.048561e-06 7.350004e-06
## 2120 7926 1608 3666 6349
## 3.726885e-07 1.238352e-04 4.406519e-04 8.651543e-06 5.408063e-05
## 3360 602 981 7291 9188
## 2.387790e-04 2.459060e-04 8.386794e-05 1.943565e-04 1.971250e-05
## 3684 2584 7234 8154 7381
## 9.003384e-05 4.012316e-04 4.198277e-04 1.426527e-06 7.559075e-06
## 7950 2546 4482 215 5643
## 1.409656e-07 1.669452e-05 6.643084e-05 2.061713e-05 3.397902e-05
## 4796 7320 4562 7756 9145
## 1.604801e-05 6.113499e-06 2.631949e-04 6.848600e-05 2.539502e-04
## 3963 8070 6763 8688 719
## 7.027402e-06 3.180469e-05 4.178068e-05 9.946228e-08 7.038299e-06
## 6371 4546 1202 6888 7389
## 6.362684e-05 9.146741e-05 4.869439e-05 4.816980e-05 1.694058e-04
## 2851 6242 6377 2972 2151
## 6.311671e-07 6.917609e-04 3.779414e-07 5.362731e-05 9.643263e-05
## 7674 3460 7267 7475 516
## 1.477307e-03 7.221570e-05 2.179706e-04 2.963032e-06 3.803949e-04
## 4422 2873 1232 3117 9120
## 2.937500e-04 5.664177e-05 3.233657e-05 3.126169e-07 1.094212e-05
## 3780 4563 4093 1863 7249
## 2.420258e-04 1.871579e-06 1.150146e-04 2.423244e-05 4.508787e-05
## 6959 2870 1611 2933 7374
## 6.858755e-05 3.235689e-04 7.617995e-07 2.054248e-05 1.060176e-03
## 6353 3470 4887 1311 5521
## 2.728707e-06 1.183098e-04 4.634961e-04 4.582865e-05 1.549543e-04
## 6407 2046 7482 2952 8716
## 1.871042e-04 2.643141e-04 1.289744e-05 2.183736e-04 1.530893e-05
## 4993 5258 755 4604 2831
## 8.462313e-06 3.530730e-05 4.924877e-10 1.492712e-04 3.219589e-04
## 9558 7727 1610 6364 3650
## 9.795744e-05 7.429858e-07 1.624528e-05 6.494312e-06 2.146988e-04
## 2525 3430 3204 5454 7527
## 3.256730e-08 1.111175e-05 1.393890e-05 7.298309e-05 1.595830e-06
## 7534 7521 3239 8955 3694
## 1.456300e-04 2.995088e-04 1.939093e-06 1.366797e-05 2.161657e-03
## 9070 8719 7648 5233 9097
## 1.527569e-04 3.977542e-05 1.757283e-05 3.061263e-05 4.964550e-07
## 424 1004 2414 857 9997
## 2.590075e-04 6.184590e-05 7.396591e-05 2.629992e-04 5.953834e-06
## 7021 9279 932 7310 9045
## 9.120386e-07 3.140234e-04 3.166925e-04 3.457938e-05 7.252833e-05
## 5715 7051 5579 1101 1349
## 1.326268e-05 6.415299e-06 9.017809e-06 3.852165e-05 1.952005e-04
## 8151 438 38 3468 7598
## 5.780132e-07 5.122936e-06 1.241996e-05 3.167856e-05 1.240119e-04
## 6132 9115 4906 7667 7412
## 7.441425e-05 1.216460e-04 9.123204e-07 3.191529e-05 2.419350e-05
## 9333 9717 9173 6182 5958
## 1.753783e-04 1.478209e-05 2.928589e-06 1.537239e-04 5.594908e-07
## 6334 2314 4360 67 8420
## 4.593751e-05 1.136030e-04 1.313428e-04 2.395343e-04 5.246034e-05
## 2698 7583 54 7413 4893
## 2.517911e-04 1.599206e-04 7.352803e-04 1.004645e-04 7.027084e-06
## 8029 8284 7360 2637 9073
## 1.397341e-04 1.277492e-05 1.575045e-04 1.631300e-04 4.236016e-04
## 5062 4983 2620 763 3212
## 1.813718e-05 7.155190e-06 3.200033e-05 6.488176e-05 1.683911e-08
## 2744 9471 2058 3200 5685
## 4.854509e-07 3.070369e-05 1.504323e-05 1.234358e-07 2.026742e-05
## 9487 6650 29 7811 7851
## 3.298805e-05 3.503598e-04 8.288766e-05 1.057256e-08 4.137148e-05
## 9121 7999 2187 3949 8976
## 2.276749e-08 8.995765e-06 1.992997e-04 2.204132e-05 2.103542e-04
## 3187 9231 6896 4912 9782
## 2.447295e-04 4.321659e-05 3.098518e-04 7.156234e-05 2.742926e-04
## 5683 1130 4466 2843 4170
## 2.796515e-04 2.325997e-06 2.100173e-04 4.820414e-05 2.401290e-04
## 9815 8986 8560 807 9650
## 6.331368e-06 1.804450e-04 6.551461e-05 8.754276e-05 6.978894e-05
## 749 5014 5392 334 6314
## 1.803523e-05 2.884737e-04 6.168260e-05 1.858631e-05 1.861155e-04
## 5093 8389 8542 1630 4692
## 4.976219e-05 1.230464e-04 1.124115e-05 1.588202e-05 7.580757e-06
## 6872 9463 213 4439 3512
## 1.965990e-05 3.301849e-08 1.641325e-03 1.718706e-05 1.826735e-04
## 6517 3163 5247 8344 3190
## 7.190662e-06 1.615420e-05 1.916583e-05 4.253797e-05 6.193759e-06
## 335 124 5953 8384 2638
## 9.025665e-04 1.237473e-04 1.052982e-04 2.541354e-07 1.341703e-04
## 4494 6103 318 4348 9119
## 2.205949e-03 1.752652e-05 5.073955e-06 1.277723e-05 2.652696e-05
## 16 906 4247 5719 5037
## 1.543603e-04 2.271936e-04 3.263342e-04 7.692329e-05 7.220569e-05
## 511 3852 6669 5657 782
## 3.661541e-05 7.141863e-04 7.468342e-04 3.698662e-05 4.874546e-05
## 4600 6376 8917 7588 2962
## 1.564299e-07 1.386889e-04 6.536168e-04 4.269636e-05 1.974766e-04
## 6783 6595 5474 7203 4631
## 6.496485e-04 2.225815e-04 4.369260e-04 1.910711e-03 4.444860e-05
## 9449 2983 4119 479 6507
## 2.395339e-04 6.398318e-05 4.167797e-04 3.439950e-05 5.516170e-04
## 1478 9824 1994 5816 7524
## 1.284932e-06 9.551535e-05 6.661372e-04 4.636706e-05 1.960797e-04
## 7015 9451 6306 4625 9713
## 4.796818e-08 6.299818e-04 4.073281e-05 7.739177e-05 9.513507e-05
## 1244 271 3235 1540 4149
## 7.179724e-04 3.379966e-05 1.001024e-05 5.155900e-05 4.045379e-04
## 5315 9017 1903 1239 2010
## 1.738429e-04 1.132996e-04 3.684519e-05 3.287943e-05 1.905084e-05
## 4476 9389 7012 3583 2161
## 9.405879e-06 1.159847e-07 1.286161e-05 2.651290e-06 2.869477e-05
## 5518 8454 1984 7763 1078
## 8.862170e-04 1.229452e-04 7.194603e-05 1.247503e-05 2.306257e-06
## 9929 3340 6069 6106 6174
## 2.784893e-05 1.480737e-05 1.648611e-04 2.646392e-06 4.697897e-05
## 5614 3682 809 825 7777
## 4.784008e-05 1.859623e-04 1.118587e-04 3.712994e-04 1.315831e-04
## 9592 7461 887 5718 4384
## 8.157040e-04 2.510840e-05 4.589916e-05 1.930724e-06 1.165909e-03
## 2091 4668 5706 9259 8357
## 7.153364e-04 5.361152e-06 2.738577e-04 4.688677e-04 5.012739e-05
## 5032 3397 7736 1156 6191
## 3.990090e-04 3.272135e-05 1.535382e-06 5.622889e-05 6.603142e-07
## 8410 7217 3386 6894 392
## 1.533443e-04 1.474362e-05 2.406382e-05 2.611503e-04 9.546264e-05
## 1757 939 341 8559 9553
## 2.110129e-05 7.007199e-05 8.172819e-05 2.131606e-05 1.114476e-05
## 6466 3821 5777 4670 2426
## 2.156259e-04 8.184619e-05 2.259351e-04 2.167648e-04 4.012563e-04
## 7952 797 4269 4955 9426
## 1.472654e-03 6.747444e-06 1.041979e-03 2.301370e-04 1.751526e-04
## 2430 3690 4623 9099 6901
## 2.551954e-05 2.628292e-05 4.811519e-06 3.253124e-04 1.522749e-03
## 8777 7718 6092 4854 2478
## 1.408760e-04 7.688794e-05 1.882682e-08 1.566240e-05 9.171658e-05
## 9502 9170 9019 8323 2772
## 3.482656e-07 8.344445e-05 1.278193e-07 1.080915e-04 5.802248e-05
## 6433 7739 4624 9427 9906
## 1.691215e-04 4.633658e-05 2.133927e-05 3.637324e-04 1.354904e-04
## 1606 4910 1810 8088 5453
## 4.303654e-05 5.094335e-04 1.640077e-03 2.131344e-05 1.998838e-04
## 9082 3481 5844 96 3965
## 8.079573e-05 1.578954e-07 5.469442e-04 1.932650e-07 6.359241e-05
## 7508 3570 3766 8747 951
## 1.045689e-05 1.051492e-07 3.604519e-07 9.389455e-06 1.151428e-04
## 3147 3750 9775 5656 7480
## 3.390605e-04 1.279111e-04 9.041019e-05 4.236278e-04 1.514564e-04
## 2799 2403 3090 1852 4078
## 5.615606e-05 2.155868e-06 1.307264e-05 2.069265e-05 1.023948e-06
## 9761 8962 8856 1303 6295
## 1.668942e-04 1.901681e-05 4.860532e-06 1.242980e-03 1.120256e-03
## 7928 1586 3783 2017 3473
## 2.095818e-04 1.701515e-04 1.707848e-04 2.632455e-04 1.732137e-04
## 8969 779 1759 6044 5497
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## 5073 6265 5126 6535 4722
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## 9879 6996 3807 4793 1939
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## 9349 7318 9465 9037 7880
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## 8 9071 7689 1103 956
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## 560 3069 5343 530 5344
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## 1.425241e-03 9.299693e-05 4.063773e-04 1.113388e-04 5.585386e-07
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## 2.016503e-05 2.950138e-05 2.037430e-04 7.130065e-05 6.949523e-05
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## 7264 744 4510 7432 7506
## 1.977810e-05 2.033714e-05 1.071781e-07 3.119330e-04 1.548378e-07
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## 5514 5480 327 5961 944
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## 8160 7178 8018 7315 7641
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## 4229 8687 99 8818 1012
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## 7258 6530 7250 5955 2829
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## 4658 7991 7 8174 74
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## 1.506669e-05 2.905397e-06 9.262778e-05 2.820745e-04 2.459553e-05
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## 4.788278e-05 1.071961e-05 7.465451e-05 3.192800e-05 2.608096e-06
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## 1.218582e-05 1.713692e-05 6.573869e-05 6.341908e-08 5.265962e-08
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## 3.301243e-06 2.318484e-05 3.210280e-04 6.862046e-05 7.250050e-05
## 693 1795 9711 8494 982
## 8.692066e-05 2.185230e-05 6.329645e-05 7.096509e-05 5.336111e-05
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## 9.788631e-05 6.261645e-05 3.076300e-06 2.989275e-04 3.104698e-04
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## 1.015875e-06 2.394280e-04 2.002258e-06 1.598016e-05 2.119514e-04
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## 7.217946e-05 6.195553e-08 5.107070e-05 2.505791e-05 3.384022e-04
## 5252 7682 257 2721 6863
## 9.595289e-04 7.407604e-05 1.580509e-05 2.854044e-05 3.757061e-07
## 8582 2062 5732 5660 1999
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## 7724 614 7603 3416 9980
## 5.685601e-05 2.600467e-04 7.648002e-05 2.707735e-05 7.863611e-04
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## 7195 5860 3269 89 9632
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## 1.688116e-04 2.949395e-04 1.703227e-05 1.619329e-04 5.755485e-05
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## 1.038646e-03 1.140655e-05 1.957738e-04 4.104949e-04 1.335731e-06
## 2511 9204 2466 3232 611
## 8.544093e-05 7.904737e-04 1.133454e-04 1.821379e-05 1.264084e-04
## 2123 8238 1194 8319 6139
## 1.233764e-05 2.690527e-04 2.409563e-06 1.368995e-06 1.265202e-04
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## 1.221349e-06 3.834224e-06 1.034934e-04 3.911026e-05 1.531718e-04
## 1162 822 2938 5228 6270
## 3.624065e-04 5.579604e-05 4.591768e-05 1.883950e-05 1.340488e-04
## 3351 3978 5623 6942 618
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## 4262 1601 1314 1384 5005
## 3.523838e-04 7.878123e-05 1.346012e-06 1.182000e-05 4.620231e-05
## 777 2956 8572 2369 9875
## 2.906202e-06 6.890281e-06 2.163635e-04 1.914044e-05 2.633315e-06
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## 1.051853e-04 1.292014e-06 1.148186e-04 2.142467e-04 5.505764e-05
## 4158 8411 3299 2748 2846
## 6.643759e-05 3.149476e-05 1.456315e-06 2.073222e-05 2.400502e-04
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## 5.039316e-05 1.321285e-07 7.221756e-05 1.140168e-03 3.563153e-04
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## 6.371785e-05 1.608209e-04 4.746310e-05 1.814834e-04 5.949845e-05
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## 2.108304e-05 2.027411e-04 7.558147e-06 1.413568e-04 2.266981e-05
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## 218 4064 4314 4182 1493
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## 8331 9203 7751 6567 2852
## 5.875605e-05 4.015007e-07 2.078375e-05 3.296431e-04 6.808063e-05
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## 2.024479e-04 8.552517e-07 1.172985e-04 2.411341e-05 6.510240e-04
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## 4.500240e-04 3.284621e-06 2.591787e-04 4.367302e-06 7.499887e-06
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## 1.004809e-03 1.360169e-03 1.491146e-03 1.339009e-04 2.531134e-04
## 2392 5184 398 726 4040
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## 7905 1659 7183 2707 9893
## 1.000946e-05 6.224509e-06 1.601879e-03 4.304188e-05 2.745674e-06
## 6504 686 7223 7307 793
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## 9193 5759 3459 9103 5076
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## 6571 7655 122 9584 2462
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## 8812 8619 6303 8543 3143
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## 4.955370e-05 2.037471e-04 1.645849e-04 1.877400e-07 7.010647e-06
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## 6017 6473 6125 3856 7097
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## 9896 7476 1989 4166 3008
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## 7671 7533 5309 5674 4765
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## 3.984631e-05 2.538179e-05 2.578894e-06 7.698861e-05 1.564432e-07
## 3145 7505 949 1804 8146
## 6.041454e-05 3.340432e-04 2.898311e-05 3.425094e-04 7.885004e-05
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## 1.318037e-04 5.436164e-04 2.764276e-05 2.426929e-05 2.394624e-05
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## 1.194507e-04 4.590121e-04 3.432654e-04 2.055954e-04 2.174909e-04
## 125 3617 2195 6568 2190
## 4.230531e-08 1.244856e-04 1.245656e-04 1.066468e-05 4.689520e-05
## 292 1151 7061 5119 4659
## 4.859826e-05 3.656842e-05 1.114394e-04 2.075046e-04 2.089518e-08
## 7376 1405 9653 4821 9142
## 2.860071e-04 8.749595e-05 9.599867e-05 1.647538e-04 2.430147e-05
## 4975 5911 4666 4537 9241
## 6.965410e-05 1.915690e-05 8.980081e-06 2.382357e-05 7.395045e-04
## 8938 7814 5648 3851 7975
## 1.310636e-04 2.715589e-04 1.617387e-03 3.369851e-05 4.188506e-04
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## 1.673467e-05 7.214871e-04 6.708914e-06 4.783968e-06 3.814690e-06
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## 980 3887 7635 5692 2619
## 5.975258e-05 8.162920e-05 9.934169e-05 8.801450e-06 1.081701e-03
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## 7165 681 8957 4233 7862
## 1.209182e-04 1.698019e-04 9.334942e-05 1.286474e-05 1.273932e-04
## 3982 9812 7444 7152 6963
## 2.880263e-05 9.463828e-05 5.809006e-04 2.285960e-04 1.551616e-04
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## 3.709409e-04 2.393916e-05 4.643381e-04 8.129866e-04 2.794326e-05
## 7262 184 4442 3479 5515
## 1.203370e-04 1.074040e-05 6.395089e-04 1.031352e-04 2.936505e-04
## 3385 8785 7467 7757 441
## 5.652445e-06 1.217798e-04 1.713990e-03 7.867828e-05 9.118772e-04
## 8885 9611 1437 7215 9302
## 4.294272e-05 3.766827e-05 3.896306e-04 8.358415e-04 1.502715e-07
## 4270 7890 5681 1864 8467
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## 4108 6243 6962 760 5303
## 1.377742e-07 7.712944e-05 4.913059e-06 1.636369e-05 3.742044e-04
## 1081 7460 2475 2663 2456
## 4.975570e-04 1.123475e-06 1.511662e-04 1.075147e-04 4.164575e-06
## 240 8739 7163 8179 6867
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## 1047 9213 1402 8880 778
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## 8337 3368 1781 4714 2788
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## 5124 5909 665 4309 7904
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## 387 2481 2493 7086 7784
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## 634 5936 6384 7495 5801
## 3.686361e-05 3.485913e-05 3.283002e-08 2.847144e-05 4.517302e-05
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## 1.649413e-05 5.312138e-06 2.263415e-05 2.197605e-03 9.148921e-05
## 4513 5194 4662 390 6624
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## 6805 4394 8182 1280 5734
## 2.339945e-05 2.017322e-05 2.072560e-04 2.466523e-04 7.368583e-04
## 1928 5382 229 3155 7104
## 2.100557e-04 3.132988e-04 1.707471e-03 3.428539e-05 1.111882e-04
## 5882 2144 119 4639 550
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## 9982 9442 9939 9423 8447
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## 5305 8253 8770 8517 5571
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## 7.974683e-04 1.592911e-05 4.736038e-04 3.135206e-04 4.093258e-07
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## 7259 5050 9406 325 4614
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## 6486 8264 7064 2157 4960
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## 1508 5056 4852 4694 3810
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## 789 3518 2135 9048 1233
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## 3.701339e-05 2.891944e-04 2.914887e-05 2.148898e-04 1.251868e-04
## 668 2520 7047 1444 2689
## 1.041263e-04 2.303175e-05 2.851704e-04 1.308475e-04 2.686617e-04
## 9829 4518 5316 1362 6985
## 2.222868e-04 2.437523e-05 2.622891e-05 4.838979e-05 2.447195e-05
## 655 630 5147 7644 3422
## 1.489892e-04 6.198173e-05 4.532859e-04 4.485601e-05 2.614482e-05
## 820 6836 8566 1809 4938
## 3.923350e-06 5.298508e-05 3.440192e-05 8.609732e-05 4.964470e-07
## 9810 7070 8015 7398 6262
## 1.764394e-05 4.549089e-07 4.140032e-06 1.352658e-04 1.220142e-04
## 1198 1260 1110 599 2155
## 1.553626e-04 7.674783e-06 2.074494e-04 1.240553e-05 1.430303e-04
## 2143 6520 3955 6012 2299
## 1.148136e-04 6.032091e-07 2.176396e-05 1.144355e-05 7.407512e-06
## 6887 147 7923 6721 1934
## 1.754194e-04 5.462654e-05 1.581254e-05 1.315964e-04 1.479698e-07
## 4580 5550 418 5581 1382
## 6.639557e-06 4.357042e-06 7.200078e-05 1.876792e-04 1.308183e-05
## 765 913 7008 3819 9176
## 4.452889e-07 1.115086e-04 3.151181e-05 9.693276e-04 6.436844e-05
## 8361 5626
## 1.327988e-05 1.701808e-04model.null2 = lm(grand.mean.formula, data.train2)
summary(model.null2)##
## Call:
## lm(formula = grand.mean.formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.1328 -6.1000 -0.6467 5.8764 28.7498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 124.0899 0.1172 1059 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.855 on 5707 degrees of freedomplot.diagnostics(model.null2, data.train2)
## hat values (leverages) are all = 0.0001751927
## and there are no factor predictors; no plot no. 5
## [1] "Number of data points that have Cook's D > 4/n: 270"
## [1] "Number of data points that have Cook's D > 1: 0"## 3167 2824 6081 3220 4244
## 5.104587e-04 5.095335e-05 1.517892e-06 6.231142e-05 7.550067e-04
## 8540 1169 2211 6546 4289
## 7.583539e-06 3.112090e-05 3.595500e-05 7.256853e-05 3.513150e-04
## 1976 8380 2866 3788 8053
## 4.568730e-05 1.897758e-05 6.506225e-05 9.880029e-04 4.516281e-04
## 9864 416 9047 9999 5828
## 8.699055e-05 3.437041e-04 1.827626e-04 9.537261e-04 5.246333e-08
## 295 7690 9633 4140 663
## 1.212587e-06 3.548050e-04 5.309429e-04 1.111900e-04 1.221798e-06
## 3196 2840 7120 90 4490
## 1.016509e-04 2.300633e-04 7.482953e-06 3.483894e-05 1.057735e-04
## 6380 967 3004 1799 3419
## 7.107811e-06 4.639854e-05 5.909726e-05 1.719774e-04 2.529187e-06
## 3587 5428 239 5688 7541
## 9.459168e-05 6.776311e-05 2.620271e-04 4.338650e-05 1.308262e-04
## 2251 3825 2835 7938 8698
## 1.638106e-05 4.536167e-04 1.074386e-06 1.469076e-04 4.647248e-04
## 7260 6975 6994 6857 7142
## 2.142320e-07 7.747684e-05 1.590484e-06 2.160143e-04 1.141951e-04
## 194 380 8328 6204 139
## 3.039400e-05 1.132685e-08 2.993660e-04 1.940358e-04 4.177571e-04
## 2906 7989 9096 1831 7750
## 2.397596e-04 7.400708e-05 6.587622e-08 2.222849e-04 1.536974e-05
## 3234 8613 6837 4075 9425
## 7.222801e-04 1.775862e-04 1.003078e-04 2.165939e-06 8.208300e-04
## 8638 6781 7776 6574 5504
## 5.903605e-07 2.191675e-04 5.996786e-05 3.979260e-04 1.445730e-05
## 2176 8304 6554 584 8509
## 9.730596e-06 5.076402e-07 3.619629e-05 8.683036e-05 1.709182e-05
## 9291 8768 2002 5639 7835
## 7.647743e-04 1.557853e-04 1.741301e-04 6.293994e-04 3.915305e-07
## 8466 7308 203 7861 5452
## 3.459431e-05 6.406615e-05 6.514016e-05 1.983398e-05 3.050858e-04
## 6130 9697 2068 8978 8209
## 2.648969e-05 5.274210e-04 7.537703e-05 6.293780e-05 1.466486e-04
## 3410 5215 6525 8052 9686
## 1.116730e-05 2.040754e-08 8.033972e-05 2.608999e-05 3.305048e-04
## 4308 8757 6043 4787 3622
## 7.062659e-06 3.605644e-06 2.737261e-04 2.265658e-04 6.255129e-06
## 2244 4837 5522 3061 526
## 2.367786e-05 2.910738e-04 2.014526e-05 5.485252e-06 3.353888e-04
## 3786 6217 4098 212 9630
## 6.454646e-05 5.211732e-04 2.027512e-04 2.382192e-04 1.874459e-04
## 3005 187 6293 4454 2505
## 2.080281e-05 1.352732e-05 4.567010e-04 2.733938e-05 1.492448e-07
## 14 371 4034 2596 7397
## 5.348778e-06 3.083061e-04 3.414720e-04 1.742585e-05 3.637558e-04
## 7538 1008 343 7313 2953
## 9.856380e-05 6.260296e-04 1.847562e-03 4.391588e-04 2.120160e-05
## 241 8008 9602 3152 8950
## 9.740123e-08 4.762697e-04 1.120779e-05 4.356577e-06 5.320332e-05
## 3087 9676 7848 5327 5763
## 2.045774e-04 1.920923e-04 5.578453e-05 1.248279e-04 9.215228e-05
## 4192 5339 540 8763 9340
## 5.025368e-04 8.801841e-05 1.956030e-04 5.024185e-05 1.165675e-05
## 3074 1134 8708 1589 6084
## 3.495256e-05 1.594956e-04 1.682585e-04 4.548811e-04 4.942538e-07
## 6545 1942 5446 3247 7894
## 4.851766e-04 4.824022e-06 7.833624e-04 8.441386e-04 9.645684e-06
## 3927 4207 3182 9715 9967
## 4.554475e-05 3.196887e-08 1.184880e-04 1.103507e-03 5.730266e-05
## 4100 9817 3655 5413 3266
## 2.489066e-04 3.188926e-04 2.210534e-04 1.198222e-03 2.822430e-04
## 82 9971 5051 8998 2630
## 1.844601e-05 1.518789e-04 1.681740e-04 6.625907e-05 8.617324e-06
## 3224 4129 2719 174 3157
## 5.747637e-04 6.195581e-04 1.672952e-06 1.030534e-03 4.866682e-05
## 4819 9305 3277 2934 8444
## 6.940667e-05 1.407688e-04 5.596730e-04 1.244308e-04 3.126185e-04
## 6684 5770 4435 236 6653
## 1.682131e-04 2.091147e-04 4.969073e-04 1.918068e-04 9.680910e-05
## 8217 2115 9091 91 3233
## 7.286177e-05 1.328320e-04 8.547369e-05 2.412429e-05 3.264120e-04
## 7729 7886 1300 1652 4021
## 1.030138e-04 1.191352e-05 1.243980e-06 5.539360e-08 9.113272e-05
## 3370 4134 3223 5997 581
## 2.021134e-04 5.918945e-05 3.279508e-05 1.699953e-05 1.351191e-07
## 2999 7105 900 3297 4812
## 4.397690e-05 3.993067e-05 8.706233e-04 3.258383e-06 9.720348e-04
## 3590 3608 704 6408 4565
## 1.056704e-04 5.243107e-05 4.485445e-04 1.208162e-03 1.279087e-04
## 3390 9420 9237 6320 2497
## 1.201279e-04 8.008905e-05 1.123052e-04 9.194077e-04 1.370619e-04
## 8697 625 1850 1277 7669
## 9.428150e-05 2.653564e-04 3.194278e-05 1.035947e-03 1.300330e-06
## 1322 5547 2708 2169 3434
## 2.497580e-04 5.879254e-05 4.779292e-05 1.255991e-05 9.556888e-04
## 1674 1752 7337 5067 9326
## 3.393670e-04 9.725136e-07 2.033421e-05 1.233636e-04 4.550800e-04
## 1014 9208 8997 3586 1594
## 1.285057e-04 3.421746e-04 2.132827e-04 2.677904e-05 1.583971e-04
## 3685 6252 7787 2798 5462
## 3.671157e-05 9.989562e-05 5.991546e-05 1.994929e-07 1.455266e-04
## 1877 6101 6175 9087 1067
## 5.505723e-06 6.749417e-04 3.383622e-05 2.538407e-05 1.709969e-04
## 1524 2908 6373 4221 1767
## 1.175254e-05 1.123375e-04 3.065670e-05 1.195585e-04 8.663604e-05
## 5125 9215 5664 5274 3130
## 1.189749e-07 1.189970e-04 7.935736e-04 5.684812e-06 1.438798e-04
## 8855 9765 8424 4886 2857
## 3.984657e-04 8.596502e-08 1.286422e-07 1.436412e-05 6.524151e-06
## 4239 6387 9932 1900 7930
## 1.826724e-08 4.718531e-06 5.545530e-04 6.888833e-04 5.645287e-05
## 1451 4883 5894 9995 9478
## 9.692909e-07 9.957603e-07 9.660623e-06 2.488716e-04 5.295583e-05
## 4150 8404 6357 9354 5086
## 7.743128e-05 5.037213e-04 1.335331e-05 9.570860e-05 1.926292e-04
## 6940 7888 679 1922 1794
## 8.524863e-04 4.174162e-04 4.381460e-04 6.509668e-05 3.454985e-04
## 5092 1579 7449 2120 7926
## 7.953358e-05 2.493556e-05 2.815445e-05 1.396981e-06 1.410632e-04
## 1608 3666 6349 3360 602
## 7.842077e-04 2.931353e-06 1.225618e-04 2.974318e-04 3.073164e-04
## 981 7291 9188 3684 2584
## 8.893965e-05 2.362293e-04 5.554092e-05 9.685222e-05 7.188071e-04
## 7234 8154 7381 7950 2546
## 5.522755e-04 2.088191e-07 2.171971e-06 5.789316e-06 4.918308e-05
## 4482 215 5643 4796 7320
## 6.691128e-05 1.367368e-05 2.806541e-05 9.205204e-06 1.277002e-06
## 4562 7756 9145 3963 8070
## 4.876643e-04 1.492095e-04 4.720275e-04 1.826606e-06 7.996184e-05
## 6763 8688 719 6371 4546
## 3.703537e-05 2.397386e-06 2.739399e-05 6.342613e-05 9.869978e-05
## 1202 6888 7389 2851 6242
## 4.521599e-05 1.114575e-04 3.276240e-04 8.563510e-06 9.434984e-04
## 6377 2972 2151 3460 7267
## 1.384426e-06 1.217141e-04 1.051203e-04 7.415549e-05 2.686706e-04
## 7475 516 4422 2873 1232
## 3.894081e-08 4.962347e-04 3.740515e-04 5.482830e-05 8.100801e-05
## 3117 9120 3780 4563 4093
## 1.551793e-06 4.696839e-06 3.019329e-04 5.823430e-08 1.294096e-04
## 1863 7249 6959 2870 1611
## 6.483464e-05 4.092490e-05 6.960385e-05 4.159317e-04 7.331224e-07
## 2933 6353 3470 4887 1311
## 5.726606e-05 1.233955e-08 1.337547e-04 6.145894e-04 1.070257e-04
## 5521 6407 2046 7482 2952
## 1.826787e-04 2.263139e-04 3.329182e-04 6.345924e-06 4.116016e-04
## 8716 4993 5258 755 4604
## 4.621250e-05 3.082264e-05 2.956953e-05 3.870985e-06 2.927401e-04
## 2831 9558 7727 1610 6364
## 4.136656e-04 1.070985e-04 7.563627e-07 4.822387e-05 1.498704e-06
## 3650 2525 3430 3204 5454
## 4.053349e-04 2.944174e-06 3.695167e-05 7.266525e-06 1.574304e-04
## 7527 7534 7521 3239 8955
## 1.230903e-05 1.701364e-04 5.488641e-04 1.346085e-05 7.024499e-06
## 9070 8719 7648 5233 9097
## 1.797179e-04 3.470043e-05 1.065989e-05 2.430298e-05 7.922928e-06
## 424 1004 2414 857 9997
## 4.805846e-04 6.122218e-05 1.592217e-04 4.873334e-04 2.469639e-05
## 7021 9279 932 7310 9045
## 9.769914e-06 4.025040e-04 5.777131e-04 8.539966e-05 7.454894e-05
## 5715 7051 5579 1101 1349
## 4.175309e-05 1.451805e-06 3.199173e-06 9.304837e-05 2.373848e-04
## 8151 438 38 3468 7598
## 9.919308e-07 2.256444e-05 5.933093e-06 2.548619e-05 2.485893e-04
## 6132 9115 4906 7667 7412
## 7.692635e-05 2.444277e-04 9.771059e-06 8.017954e-05 1.736578e-05
## 9333 9717 9173 5958 6334
## 2.103352e-04 4.507314e-05 3.417910e-08 8.229156e-06 4.193137e-05
## 2314 4360 67 8420 2698
## 1.275515e-04 2.614536e-04 2.984787e-04 4.974599e-05 4.683720e-04
## 7583 54 7413 4893 8029
## 1.893815e-04 1.006664e-03 2.069269e-04 2.736651e-05 1.622360e-04
## 8284 7360 2637 9073 5062
## 6.239411e-06 3.070341e-04 1.937210e-04 7.559468e-04 5.223995e-05
## 4983 2620 763 3212 2744
## 1.908021e-06 2.584488e-05 6.498366e-05 3.164158e-06 7.868136e-06
## 9471 2058 3200 5685 9487
## 2.440376e-05 8.270106e-06 5.646101e-06 1.332087e-05 2.695021e-05
## 29 7811 7851 9121 7999
## 8.768701e-05 4.274950e-06 3.655739e-05 3.071539e-06 3.207998e-05
## 2187 3949 8976 3187 9231
## 2.430012e-04 6.035922e-05 2.581826e-04 3.056836e-04 3.871845e-05
## 6896 4912 9782 5683 1130
## 5.662364e-04 1.548376e-04 3.468367e-04 5.154404e-04 2.143870e-09
## 4466 2843 4170 9815 8986
## 2.577191e-04 1.115223e-04 4.486022e-04 2.564536e-05 3.466531e-04
## 8560 807 9650 749 5014
## 1.437543e-04 9.364869e-05 1.515955e-04 5.202504e-05 3.666623e-04
## 5392 334 6314 5093 8389
## 1.366892e-04 5.318481e-05 2.249641e-04 1.144605e-04 1.400182e-04
## 8542 1630 4692 6872 9463
## 3.724439e-05 9.049373e-06 2.186415e-06 1.271181e-05 2.938868e-06
## 4439 3512 6517 3163 5247
## 5.023063e-05 3.504868e-04 1.930805e-06 4.802895e-05 1.222024e-05
## 8344 3190 124 5953 8384
## 1.007601e-04 2.530076e-05 1.409468e-04 1.166610e-04 6.583600e-06
## 2638 6103 318 4348 9119
## 1.548039e-04 1.061513e-05 7.342464e-07 4.068066e-05 6.946925e-05
## 16 906 4247 5719 5037
## 1.818781e-04 2.813999e-04 5.938723e-04 1.646010e-04 7.414290e-05
## 511 6669 5657 782 4600
## 8.936050e-05 1.023454e-03 3.148558e-05 4.527710e-05 2.099169e-06
## 6376 8917 7588 2962 6595
## 2.743015e-04 1.134555e-03 1.010627e-04 3.758945e-04 2.750306e-04
## 4631 9449 2983 4119 479
## 1.044034e-04 2.984781e-04 1.409350e-04 7.446283e-04 2.854041e-05
## 6507 1478 9824 5816 7524
## 9.672928e-04 1.120487e-05 1.980929e-04 4.244129e-05 2.385889e-04
## 7015 9451 6306 4625 9713
## 2.782198e-06 8.540481e-04 3.581290e-05 1.654517e-04 1.034393e-04
## 1244 271 3235 1540 4149
## 1.239689e-03 2.786312e-05 3.953881e-06 4.865750e-05 7.243009e-04
## 5315 9017 1903 1239 2010
## 2.082481e-04 1.271524e-04 3.132362e-05 8.207390e-05 1.210633e-05
## 4476 9389 7012 3583 2161
## 3.489443e-06 5.582736e-06 4.086750e-05 1.569455e-05 2.219478e-05
## 8454 1984 7763 1078 9929
## 2.467137e-04 1.555382e-04 5.980394e-06 2.954405e-09 2.127399e-05
## 3340 6069 6106 6174 5614
## 8.053557e-06 3.197711e-04 6.385736e-09 1.092058e-04 4.419515e-05
## 3682 809 825 7777 7461
## 2.247550e-04 2.271571e-04 4.833428e-04 2.618746e-04 6.660984e-05
## 887 5718 4384 2091 4668
## 4.188588e-05 1.343346e-05 1.636670e-03 1.235388e-03 2.318231e-05
## 5706 9259 8357 5032 3397
## 3.462295e-04 8.308932e-04 1.151480e-04 7.151131e-04 2.665113e-05
## 7736 1156 6191 8410 7217
## 1.611434e-07 1.265704e-04 8.695815e-06 1.805091e-04 4.498973e-05
## 3386 6894 392 1757 939
## 6.449203e-05 4.842081e-04 1.038635e-04 1.416473e-05 7.146288e-05
## 341 8559 9553 6466 3821
## 1.733080e-04 1.438350e-05 3.702639e-05 4.069164e-04 8.635786e-05
## 5777 4670 2426 797 4955
## 2.796612e-04 2.670086e-04 7.188482e-04 1.651974e-06 2.854686e-04
## 9426 2430 3690 4623 9099
## 2.100283e-04 6.744049e-05 1.958489e-05 6.140177e-07 5.921606e-04
## 8777 7718 6092 4854 2478
## 2.781189e-04 1.645368e-04 4.453332e-06 8.843998e-06 1.912909e-04
## 9502 9170 9019 8323 2772
## 1.457323e-06 1.764087e-04 2.238091e-06 1.203158e-04 5.651762e-05
## 6433 7739 4624 9427 9906
## 3.271332e-04 4.240508e-05 5.891383e-05 4.726281e-04 2.687126e-04
## 1606 4910 8088 5453 9082
## 3.850692e-05 6.803896e-04 1.438083e-05 3.800169e-04 8.501901e-05
## 3481 5844 96 3965 7508
## 2.092524e-06 7.342852e-04 1.943478e-06 6.338345e-05 4.306128e-06
## 3570 3766 8747 951 3147
## 5.487518e-06 1.426799e-06 3.299968e-05 1.295785e-04 4.377639e-04
## 3750 9775 5656 7480 2799
## 2.554373e-04 9.733696e-05 7.559903e-04 1.779670e-04 1.264347e-04
## 2403 3090 1852 4078 9761
## 1.365839e-08 6.498909e-06 1.375008e-05 1.021652e-05 1.988181e-04
## 8962 8856 7928 1586 3783
## 5.408762e-05 6.358940e-07 2.571202e-04 2.032352e-04 3.300047e-04
## 2017 3473 8969 779 1759
## 3.314294e-04 3.341951e-04 4.073111e-05 1.267864e-03 1.036898e-04
## 6044 5497 5703 7978 1811
## 3.486168e-07 2.512188e-05 1.064729e-04 5.262869e-05 5.180569e-05
## 7745 4383 6999 1963 4156
## 1.223100e-05 2.625813e-05 2.852654e-05 1.461580e-06 1.433694e-05
## 2088 9528 7417 9763 2308
## 9.995924e-07 1.366509e-06 4.366855e-05 5.712071e-05 1.174922e-04
## 1360 804 1452 7429 6973
## 1.573673e-04 9.406271e-04 4.857250e-07 5.605595e-05 3.674410e-06
## 8142 4484 3860 8510 7818
## 3.901699e-05 1.237094e-04 2.878771e-04 5.773642e-04 5.789175e-11
## 4519 7033 1734 2225 6379
## 6.188403e-05 7.450811e-06 3.447811e-04 8.587756e-05 4.263731e-05
## 7125 6575 1937 9207 103
## 1.136414e-04 3.775014e-05 3.598724e-04 6.085264e-05 8.368640e-05
## 2196 7220 4567 2720 4926
## 3.219896e-05 6.009287e-05 2.230171e-05 7.629273e-05 5.588573e-06
## 968 7141 2932 1241 2142
## 1.029505e-04 7.030603e-05 1.046541e-04 4.251191e-05 1.251161e-04
## 8546 9745 9381 6505 4880
## 7.183879e-05 3.266602e-05 3.798187e-04 1.077685e-04 1.737665e-04
## 250 9606 136 402 6726
## 7.576403e-07 1.841690e-04 4.365613e-05 4.777041e-05 3.935328e-04
## 7542 2675 3177 1505 5298
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## 4804 1981 3039 218 4064
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## 2.338032e-06 1.201059e-04 2.745925e-04 6.095903e-06 4.046610e-07
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## 7751 6567 2852 2658 2611
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## 1.324201e-04 6.459281e-05 1.130314e-03 1.380635e-04 1.957715e-05
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## 5780 7205 6663 5902 268
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## 8812 8619 6303 8543 3143
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## 7084 5574 2726 7274 5533
## 1.810134e-04 7.665150e-06 2.281168e-04 1.822931e-05 8.928202e-05
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## 3.672841e-05 2.923799e-04 2.476065e-06 6.915579e-06 7.355082e-04
## 6456 600 6126 9517 5331
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## 6921 6218 7458 6986 6202
## 4.624542e-05 3.866276e-04 1.956901e-04 1.965451e-06 2.732623e-05
## 7568 6074 8155 7500 3628
## 1.305556e-05 2.518562e-04 4.332739e-05 9.768445e-05 6.259700e-04
## 3948 1 6062 3890 519
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## 2065 2548 8004 4385 1859
## 1.280897e-04 1.718691e-04 4.977969e-04 1.180910e-05 1.250141e-04
## 5872 94 4515 743 2237
## 2.222201e-06 4.855733e-04 1.421398e-04 5.770752e-06 3.283643e-05
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## 4.914647e-04 3.460391e-04 3.231352e-04 2.286510e-07 7.366938e-05
## 8254 2186 5616 2344 6740
## 2.550204e-04 1.149258e-04 5.292085e-05 2.168524e-04 8.564980e-05
## 7345 546 7270 3863 3268
## 2.913403e-04 2.225939e-04 1.503781e-04 1.091884e-04 1.598739e-04
## 5682 9876 7679 5080 1112
## 2.271970e-04 3.344675e-05 3.369566e-04 1.569514e-04 8.536372e-05
## 7392 3945 3715 769 8271
## 2.464092e-04 1.683415e-04 2.558844e-05 1.470289e-05 2.019362e-05
## 4862 5723 4203 8628 9210
## 2.832747e-06 4.225897e-04 6.065179e-05 1.951422e-04 8.212655e-05
## 1700 5461 8329 5495 3475
## 2.785743e-04 1.320245e-05 2.430365e-05 1.073023e-03 1.322270e-06
## 9473 8225 4187 4878 4506
## 3.164839e-04 4.095497e-09 7.388014e-05 5.966107e-06 3.725664e-05
## 5694 5320 8845 1571 1553
## 2.686669e-05 2.250943e-04 2.490135e-05 2.425099e-04 7.655970e-04
## 5153 2482 1212 4370 3559
## 3.776626e-04 1.048496e-05 1.070409e-04 1.814182e-04 4.005314e-05
## 1730 3922 7602 3435 5205
## 2.866568e-05 4.446147e-05 4.175691e-05 4.203548e-08 4.209206e-06
## 558 8644 9205 3100 9412
## 4.273617e-07 1.811494e-05 3.522960e-04 2.645990e-07 1.320795e-04
## 8300 945 3429 7555 2920
## 2.053004e-04 5.182937e-05 4.701964e-06 5.276556e-04 6.543009e-06
## 2965 6298 8843 1467 924
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## 4.614316e-06 3.571840e-05 1.995105e-05 2.995350e-05 7.710000e-07
## 8993 1938 6361 2832 220
## 5.409090e-05 2.010914e-04 1.909820e-04 6.353030e-05 4.398082e-05
## 7053 3591 1577 6425 969
## 1.256209e-04 1.774891e-05 3.196681e-05 2.845134e-04 7.646575e-05
## 4696 8745 6494 3896 5988
## 1.566576e-04 1.184825e-04 1.013668e-04 6.877935e-05 9.333307e-05
## 1818 3423 3337 5607 2087
## 2.960175e-04 9.224136e-09 3.758091e-06 7.820473e-04 2.093986e-05
## 4802 8970 8035 5138 2973
## 1.385877e-06 2.283539e-04 3.036072e-04 6.180363e-04 3.180193e-04
## 4260 7618 9514 2659 9201
## 2.126339e-06 4.072647e-06 6.916008e-07 1.100971e-04 1.264617e-08
## 786 8438 6143 696 8895
## 8.906175e-05 1.091053e-04 2.472029e-04 3.456802e-05 1.310484e-04
## 889 8567 4271 7918 1133
## 3.687616e-06 2.036679e-04 4.765397e-04 4.453454e-05 7.112668e-05
## 3172 8503 1624 5427 4514
## 6.778923e-06 5.626924e-05 1.345850e-04 5.816320e-05 3.904173e-07
## 7424 8965 3138 2967 3557
## 1.892210e-04 3.236617e-05 1.055434e-06 2.825791e-06 1.601151e-04
## 6739 7512 4823 5195 8981
## 2.039482e-05 9.800590e-04 3.501526e-04 3.782440e-04 1.545685e-06
## 8780 2333 1457 9543 5735
## 2.256129e-05 1.564220e-04 4.434818e-05 2.076669e-04 6.170184e-04
## 5766 4932 9642 9911 4291
## 1.387763e-03 6.326207e-05 1.007309e-03 1.179421e-04 7.175309e-04
## 4553 486 5188 9958 5106
## 2.188468e-05 2.262803e-05 3.423920e-05 2.298001e-04 4.606684e-04
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## 3656 1796 3886 5878 1805
## 3.436253e-06 1.133836e-05 2.656528e-06 3.108202e-04 1.322861e-04
## 6470 5725 2943 7612 4789
## 4.620619e-05 5.241017e-04 8.433732e-06 3.948489e-06 1.961086e-04
## 4313 7305 4843 5149 1267
## 1.100811e-06 3.262662e-07 1.114547e-05 2.141411e-04 2.408874e-06
## 7687 8286 2006 198 1190
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## 7456 9264 2229 638 4000
## 9.356013e-07 9.769903e-04 4.577673e-04 4.036604e-04 3.122012e-04
## 4079 813 8735 9510 7290
## 3.265351e-04 1.193726e-05 5.887115e-05 7.297479e-05 1.027119e-04
## 5907 5812 1653 9152 4353
## 1.853251e-04 3.519235e-04 1.307634e-04 5.573986e-05 3.114963e-05
## 2291 1647 209 691 4240
## 7.603107e-04 8.910383e-05 1.583976e-04 7.086848e-05 6.894745e-04
## 4925 4124 1582 10 6757
## 7.688653e-05 2.919742e-08 4.320379e-04 1.717139e-06 8.307087e-04
## 5883 7474 2098 1746 3383
## 1.587545e-04 1.563083e-05 1.601690e-05 3.705940e-05 1.698555e-05
## 9161 9890 1168 1605 7248
## 3.929920e-04 2.822097e-06 3.139170e-05 6.597049e-05 4.419115e-05
## 7566 7969 6152 2459 9957
## 1.827929e-05 4.869789e-05 6.551116e-05 4.769483e-04 3.926224e-04
## 9737 361 142 3592 4388
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## 7383 4287 9062 3248 1337
## 2.665859e-04 3.198712e-05 1.723876e-04 1.383550e-04 3.556622e-04
## 2425 819 3818 6498 9677
## 1.010211e-05 4.256443e-05 5.813888e-04 1.402779e-04 7.193226e-05
## 7171 3761 2136 6023 4856
## 1.447982e-04 3.926602e-04 2.864739e-06 1.066542e-05 2.172104e-04
## 5758 3040 3877 2328 6036
## 8.825244e-04 3.897077e-04 2.263885e-04 1.068759e-04 3.750399e-06
## 5761 4163 8001 6097 3671
## 4.314549e-04 2.804093e-04 2.152674e-06 6.038425e-05 2.118960e-05
## 6910 2490 6142 4250 4033
## 1.054340e-04 4.987608e-04 1.303542e-07 2.174110e-04 1.093676e-05
## 7017 3282 3910 8266 9868
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## 9.224429e-06 1.031819e-04 3.124236e-05 1.266329e-05 9.791694e-05
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## 5886 9820 8309 6017 6473
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## 6125 3856 9896 7476 1989
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## 3008 9952 97 3843 6238
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## 3399 9367 4750 689 5540
## 1.336592e-04 2.822191e-04 2.499163e-04 8.258088e-05 6.468292e-06
## 6188 9137 3944 1615 4112
## 1.840480e-04 1.416038e-06 4.804334e-05 7.202534e-05 7.969056e-06
## 448 9508 6047 7846 5419
## 4.449107e-05 5.133502e-07 1.020519e-06 4.227074e-05 5.006733e-05
## 7189 4501 1483 2220 3033
## 9.355223e-05 3.651095e-05 2.051605e-04 1.243164e-05 1.043513e-03
## 55 3804 1258 3581 3853
## 9.383440e-05 6.494840e-04 1.890443e-04 3.744823e-07 2.961435e-04
## 2963 7197 3995 6213 3594
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## 2346 1766 2896 2722 8241
## 2.993349e-07 3.353458e-04 1.596017e-07 1.136445e-04 1.484002e-05
## 9767 1658 2761 1959 9944
## 2.103928e-06 2.892600e-05 3.941970e-05 8.792777e-06 3.196900e-05
## 7439 8350 8445 7628 823
## 3.030191e-04 5.747033e-04 4.627714e-05 6.031522e-04 8.722868e-06
## 2978 7944 8974 7753 6944
## 1.246403e-04 1.543403e-06 4.866195e-04 2.175963e-05 2.269240e-04
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## 3304 9862 6772 5136 6588
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## 308 1063 565 9483 3697
## 2.223613e-07 2.384951e-04 2.249326e-05 9.517192e-05 4.311359e-04
## 5476 6927 9020 7847 870
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## 1.450403e-05 7.532488e-11 2.637251e-04 1.644275e-04 1.004497e-04
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## 1550 3463 2204 2745 4555
## 2.427360e-04 2.379614e-05 1.014882e-04 6.002243e-04 1.777117e-04
## 7377 8056 4168 1992 9921
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## 7873 8302 9804 7319 9016
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## 1189 7663 2093 7759 8243
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## 7533 5309 4765 8324 4757
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## 4147 7056 8112 1464 125
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## 9842 6667 1713 856 6121
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## 6990 246 7854 9104 5804
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## 4460 8556 6749 5896 7262
## 6.683963e-04 6.423857e-05 8.234052e-04 7.230640e-05 1.364329e-04
## 184 4442 3479 3385 8785
## 4.533434e-06 1.111470e-03 2.116817e-04 1.024172e-06 1.383413e-04
## 7757 8885 9611 1437 9302
## 1.677858e-04 1.015332e-04 9.139975e-05 5.093389e-04 2.127556e-06
## 4270 7890 5681 1864 8467
## 5.459673e-05 1.461241e-04 1.716052e-05 1.388868e-05 5.193391e-06
## 4108 6243 6962 760 5303
## 2.187627e-06 1.649754e-04 2.201521e-05 9.502979e-06 4.874588e-04
## 1081 7460 2475 2663 2456
## 6.633554e-04 3.892278e-07 2.960339e-04 1.195605e-04 2.001438e-05
## 240 8739 7163 8179 6867
## 5.723510e-05 1.529673e-06 2.208363e-04 3.348894e-06 1.302519e-04
## 1047 9213 1402 8880 778
## 4.523451e-04 8.154714e-05 2.264301e-04 2.483893e-05 5.359034e-04
## 8337 3368 1781 4714 2788
## 1.399469e-06 4.221499e-05 5.188453e-05 6.545096e-06 3.497709e-05
## 3898 8327 3455 3964 5124
## 6.493015e-05 1.549156e-05 6.952905e-05 9.949410e-07 1.739628e-07
## 5909 665 4309 7904 387
## 2.871609e-04 2.093668e-05 1.015233e-06 4.370517e-05 5.418456e-05
## 7086 7784 634 5936 6384
## 1.548537e-04 1.466817e-04 8.984177e-05 2.906086e-05 2.941079e-06
## 7495 5801 2107 8769 5340
## 2.195111e-05 1.057808e-04 5.810413e-05 1.947430e-05 2.709408e-04
## 1619 8206 134 9928 7073
## 2.606508e-04 4.123701e-04 9.626559e-06 2.305564e-05 6.157528e-05
## 1331 4513 5194 4662 390
## 1.908831e-04 5.270319e-05 5.868025e-04 2.558248e-04 2.275557e-04
## 6624 6805 4394 8182 1280
## 4.178716e-05 1.653374e-05 1.322610e-05 3.926265e-04 3.083523e-04
## 5734 1928 5382 3155 7104
## 1.270490e-03 2.577719e-04 4.014854e-04 8.482576e-05 1.243775e-04
## 5882 2144 119 4639 9982
## 9.205765e-06 9.039454e-05 1.867646e-04 6.833912e-05 1.225754e-03
## 9442 9939 9423 8447 5305
## 1.777885e-07 2.874450e-04 2.769135e-04 9.101603e-05 1.318736e-04
## 8253 8770 8517 5571 8090
## 1.340542e-06 3.236125e-04 3.445910e-04 1.155997e-04 1.369200e-03
## 2125 9168 2219 320 8188
## 9.093526e-06 6.290469e-04 4.017971e-04 7.476398e-06 1.045108e-04
## 7085 6913 9738 4742 1172
## 3.065461e-04 3.559315e-06 1.207294e-04 7.946913e-05 7.721506e-04
## 5090 5699 7259 5050 9406
## 2.759679e-04 2.211550e-04 2.502771e-06 4.980759e-05 1.030984e-04
## 325 4614 6486 8264 7064
## 2.208916e-05 2.725426e-04 1.055330e-03 8.261343e-05 1.306425e-04
## 2157 4960 8930 1927 2423
## 7.064610e-08 2.149685e-04 6.847361e-04 8.031041e-06 5.435405e-05
## 8131 4929 3349 5973 8189
## 3.575874e-05 1.772454e-04 3.168242e-05 1.521482e-07 8.603640e-07
## 7941 2415 6009 404 4373
## 5.422048e-04 1.373403e-04 2.116255e-04 3.223045e-05 1.531376e-04
## 2324 8465 6897 2867 9591
## 7.700634e-05 5.659700e-05 5.476487e-05 2.627805e-04 3.605052e-05
## 5745 8340 3286 1488 4672
## 9.440498e-06 4.568650e-07 1.294977e-05 1.244521e-04 1.832670e-06
## 2189 6506 7111 6719 4410
## 1.473082e-04 7.380274e-06 5.057895e-06 3.077786e-05 1.301658e-06
## 36 8791 1207 2897 1235
## 3.588843e-05 7.011707e-04 1.404635e-07 3.462198e-05 5.264430e-05
## 235 8200 53 3605 2041
## 1.075085e-03 5.338982e-04 1.551738e-04 3.325441e-04 8.083082e-06
## 3837 8170 9124 2334 2892
## 2.292495e-04 2.104060e-04 7.042611e-06 9.950938e-05 2.286507e-04
## 2789 6712 6889 210 5551
## 6.431118e-05 3.981717e-05 5.167033e-05 2.918093e-04 6.090810e-05
## 6039 3262 3981 357 1646
## 4.556279e-04 4.035844e-05 2.423761e-04 3.257485e-04 1.959995e-05
## 3497 1030 8945 6611 1822
## 3.936799e-04 3.358836e-05 3.115609e-04 6.718952e-04 4.826107e-05
## 6752 7749 195 1687 8725
## 6.521025e-05 4.373666e-05 2.443877e-04 5.912763e-05 1.020125e-05
## 101 5222 9585 6622 3017
## 7.549300e-05 2.652892e-04 1.566751e-06 8.314981e-05 7.567698e-06
## 1129 764 5807 7634 1068
## 4.821212e-07 4.227707e-04 1.447901e-04 1.320263e-03 4.604258e-04
## 9441 6537 129 8910 1559
## 6.953212e-05 1.491506e-04 6.220295e-04 2.077148e-04 1.729151e-05
## 8452 4577 1508 5056 4852
## 1.019918e-04 3.776456e-07 1.572897e-05 2.499921e-05 8.387324e-05
## 4694 3810 3518 2135 9048
## 1.701949e-04 5.164861e-04 9.090939e-05 4.374573e-05 6.221986e-05
## 1233 4997 9245 6609 6716
## 1.065449e-05 2.255802e-04 4.285202e-06 4.921887e-04 9.441557e-07
## 4369 3795 3260 4393 5985
## 1.583374e-05 2.431869e-05 3.255797e-05 6.200542e-08 7.278337e-05
## 7434 4718 1950 1309 5976
## 5.961643e-05 1.633111e-04 2.584024e-04 3.736090e-05 9.812677e-06
## 8165 3858 3523 1862 3123
## 2.978379e-04 9.596978e-06 4.143935e-04 1.071824e-04 3.872253e-05
## 7423 6090 5393 7898 1462
## 9.195658e-04 4.669172e-06 6.483635e-05 2.117508e-06 2.965306e-05
## 2738 9615 7385 5272 5358
## 2.458046e-05 3.499317e-05 2.146032e-04 1.022442e-04 2.716034e-04
## 1807 8941 1575 1045 4444
## 1.772033e-04 4.640811e-06 9.186866e-05 4.749327e-05 1.577030e-05
## 3915 4583 6754 1002 9444
## 6.582339e-05 1.746928e-05 8.454684e-04 3.320571e-05 3.392496e-04
## 7049 9872 814 5148 2044
## 1.405655e-05 7.745089e-06 3.239224e-04 1.971142e-05 3.215905e-05
## 8640 853 7129 4884 6037
## 5.648678e-04 1.279620e-04 1.801586e-04 3.556433e-04 3.500511e-04
## 9847 1771 3806 9533 127
## 3.433094e-04 1.494063e-05 7.323578e-05 4.657296e-05 6.535507e-09
## 3315 9757 8223 6247 8152
## 1.727277e-04 8.083873e-05 2.297158e-05 6.134832e-05 9.671977e-05
## 9563 462 128 1496 4882
## 2.085010e-05 3.626012e-04 2.773990e-04 6.843596e-04 1.190217e-04
## 8626 7430 2681 1072 9572
## 5.829554e-04 4.192739e-04 4.840908e-07 6.821089e-05 1.540723e-05
## 5173 4588 6299 6049 6289
## 7.472870e-05 1.205014e-05 1.687718e-03 3.145186e-06 1.195509e-04
## 6932 1076 5334 1555 1761
## 6.576823e-05 6.941700e-04 7.099937e-07 6.232135e-05 2.938262e-05
## 5893 6864 736 9546 5738
## 1.818196e-06 2.117893e-04 1.813763e-05 5.074155e-05 3.223502e-04
## 3579 8111 5290 2787 572
## 7.200702e-04 1.170043e-03 1.140807e-05 4.300527e-07 6.494972e-05
## 7871 3515 829 5951 587
## 1.229253e-03 2.192261e-04 8.584747e-06 8.253608e-05 7.855809e-05
## 6116 8516 1390 1548 9122
## 2.587717e-04 7.938915e-05 3.311106e-04 4.429672e-06 1.185870e-10
## 5619 700 9306 5268 7309
## 1.800002e-04 1.187184e-04 3.368297e-04 1.207150e-05 1.525785e-04
## 7661 5350 9149 8093 2618
## 2.543241e-04 1.034357e-05 6.907888e-04 7.244497e-05 2.179417e-04
## 7468 3264 867 350 5183
## 1.077703e-05 1.863377e-08 9.922558e-08 3.003135e-04 1.013327e-04
## 4176 4708 472 422 7838
## 5.533853e-04 6.096360e-05 7.245730e-06 1.140222e-03 1.268321e-04
## 4329 6742 3414 8282 5691
## 4.933574e-05 2.529123e-04 1.100748e-04 5.525963e-05 1.620799e-04
## 6573 9948 3662 8473 705
## 4.510496e-04 2.130607e-05 7.085106e-04 6.045246e-04 6.303676e-05
## 6725 7810 324 3828 9870
## 1.879407e-04 2.788765e-04 1.325571e-04 7.830641e-06 6.577018e-05
## 7695 2387 386 9656 7135
## 5.328147e-07 5.535377e-05 1.640203e-04 1.518310e-04 4.948306e-04
## 3709 4747 5398 4415 7127
## 1.268772e-05 5.840193e-06 2.117568e-04 3.143352e-07 4.983608e-04
## 5670 9664 5508 1161 7179
## 3.077371e-05 2.139911e-04 3.812626e-06 4.162381e-05 3.284254e-04
## 617 3303 4954 6321 8373
## 5.666536e-05 2.110367e-04 1.716934e-04 5.492289e-04 4.103878e-06
## 5603 9461 2914 1919 5757
## 3.045364e-06 5.449714e-05 2.729276e-05 6.073557e-05 1.859064e-04
## 9596 8277 3553 9492 3469
## 1.326945e-04 2.991505e-05 1.799503e-04 1.340599e-04 3.867260e-05
## 8475 2803 9277 9947 2126
## 9.594449e-04 1.088070e-04 5.836843e-05 2.355938e-05 2.538970e-04
## 1888 5082 942 8081 167
## 3.319169e-05 4.807492e-06 1.650351e-04 3.471861e-05 7.241091e-05
## 3289 5979 3929 8927 3578
## 1.920755e-04 4.798711e-04 6.336085e-06 9.540688e-06 3.261775e-06
## 6834 4087 2496 3032 3941
## 1.534861e-05 1.489232e-04 1.278229e-04 3.082823e-05 1.591148e-04
## 2692 8453 8478 230 5488
## 3.036743e-06 6.148167e-05 6.474632e-05 1.928606e-05 9.289689e-05
## 5068 6812 4165 5482 4409
## 2.261650e-08 1.239506e-04 4.491775e-05 1.856529e-04 3.097575e-04
## 6949 9495 8194 2168 6659
## 1.793662e-04 5.443253e-05 5.388147e-05 1.180868e-04 1.127166e-04
## 731 3215 310 6409 6224
## 4.048971e-04 6.109115e-06 2.973751e-05 3.768879e-05 2.832893e-05
## 6487 1628 4764 9768 6698
## 3.054937e-06 1.785676e-06 7.440045e-05 1.507420e-04 2.342163e-04
## 7296 7492 7199 6105 9984
## 6.598793e-05 1.082766e-04 5.320704e-04 3.885828e-04 3.175761e-05
## 6423 9307 3601 6288 9795
## 2.871583e-07 1.485296e-07 1.972816e-04 4.229525e-05 4.867770e-05
## 7573 7525 7892 7072 8352
## 1.113708e-04 2.097286e-04 3.276671e-04 5.631407e-06 1.316478e-05
## 1565 6751 8097 5610 5431
## 4.340291e-06 7.374293e-06 2.748354e-07 3.213708e-05 1.735800e-04
## 9199 2060 7883 3833 4941
## 2.923893e-04 1.626432e-04 4.778466e-05 3.151625e-05 5.315150e-04
## 3861 1556 9407 668 2520
## 2.269145e-05 4.056608e-04 1.428551e-04 2.134442e-04 6.238865e-05
## 7047 1444 2689 9829 4518
## 3.620397e-04 1.503767e-04 4.968995e-04 2.746238e-04 1.755712e-05
## 5316 1362 6985 655 630
## 1.952701e-05 1.118729e-04 6.532078e-05 1.746483e-04 6.139001e-05
## 7644 3422 820 6836 8566
## 1.051783e-04 1.943696e-05 2.697863e-07 5.038087e-05 2.854316e-05
## 1809 4938 9810 7070 8015
## 1.811925e-04 7.922888e-06 1.072870e-05 7.713752e-06 3.438768e-07
## 7398 6262 1198 1260 1110
## 2.683199e-04 2.450758e-04 3.033196e-04 2.894057e-05 3.929570e-04
## 599 2155 2143 6520 3955
## 3.985531e-05 1.666498e-04 2.323810e-04 9.518005e-07 5.978889e-05
## 6012 2299 6887 147 7923
## 3.770118e-05 2.829410e-05 3.379979e-04 1.235817e-04 8.984297e-06
## 6721 1934 4580 5550 418
## 1.513738e-04 2.138365e-06 2.641198e-05 4.248128e-07 1.556381e-04
## 5581 1382 765 913 7008
## 3.590899e-04 6.506952e-06 7.664383e-06 2.265376e-04 2.530057e-05
## 9176 8361 5626
## 6.434612e-05 6.680877e-06 3.289621e-04Variable Selection
http://www.stat.columbia.edu/~martin/W2024/R10.pdf
Forward Selection (w/ full train)
Train
if (algo.forward == TRUE){
t1 = Sys.time()
model.forward = step(model.null, scope=list(lower=model.null, upper=model.full), direction="forward", trace = 0)
print(summary(model.forward))
#saveRDS(model.forward,file = "model_forward.rds")
t2 = Sys.time()
print (paste("Time taken for Forward Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.forward, data.train)
}Test
if (algo.forward == TRUE){
test.model(model.forward, data.test, "Forward Selection")
}Forward Selection (w/ filtered train)
Train
if (algo.forward == TRUE){
t1 = Sys.time()
model.forward2 = step(model.null2, scope=list(lower=model.null2, upper=model.full2), direction="forward", trace = 0)
print(summary(model.forward2))
#saveRDS(model.forward,file = "model_forward.rds")
t2 = Sys.time()
print (paste("Time taken for Forward Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.forward2, data.train2)
}Test
if (algo.forward == TRUE){
test.model(model.forward2, data.test, "Forward Selection (2)")
}Backward Elimination
Train
if (algo.backward == TRUE){
# Takes too much time
t1 = Sys.time()
model.backward = step(model.full, data = data.train, direction="backward", trace = 0)
print(summary(model.backward))
#saveRDS(model.forward,file = "model_backward.rds")
t2 = Sys.time()
print (paste("Time taken for Backward Elimination: ",t2-t1, sep = ""))
plot.diagnostics(model.backward, data.train)
}Test
if (algo.backward == TRUE){
test.model(model.backard, data.test, "Backward Elimination")
}Stepwise Selection (w/ full train)
Train
if (algo.stepwise == TRUE){
t1 = Sys.time()
model.stepwise = step(model.null, scope=list(upper=model.full), data = data.train, direction="both", trace = 0)
print(summary(model.stepwise))
#saveRDS(model.stepwise,file = "model_stepwise.rds")
t2 = Sys.time()
print (paste("Time taken for Stepwise Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.stepwise, data.train)
}##
## Call:
## lm(formula = y3 ~ sqrt.x18 + x7 + stat98 + stat110 + x9 + x17 +
## x16 + x4 + stat14 + x10 + x11 + x8 + x21 + x14 + stat41 +
## stat4 + stat23 + stat3 + stat60 + stat100 + stat144 + stat33 +
## stat200 + stat149 + x13 + stat26 + stat24 + stat151 + stat175 +
## stat126 + stat146 + stat92 + stat22 + stat205 + stat135 +
## stat25 + stat73 + stat55 + stat46 + x19 + stat84 + stat19 +
## stat217 + stat76 + stat13 + stat156 + stat104, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.786 -6.236 -1.745 4.481 54.050
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.687e+01 2.435e+00 35.670 < 2e-16 ***
## sqrt.x18 7.311e+00 2.678e-01 27.297 < 2e-16 ***
## x7 3.206e+00 1.807e-01 17.739 < 2e-16 ***
## stat98 1.063e+00 6.912e-02 15.382 < 2e-16 ***
## stat110 -9.582e-01 7.009e-02 -13.671 < 2e-16 ***
## x9 9.302e-01 9.440e-02 9.854 < 2e-16 ***
## x17 4.553e-01 9.240e-02 4.927 8.57e-07 ***
## x16 2.905e-01 6.076e-02 4.782 1.78e-06 ***
## x4 -1.166e-02 2.562e-03 -4.550 5.47e-06 ***
## stat14 -2.764e-01 6.954e-02 -3.974 7.14e-05 ***
## x10 3.302e-01 8.743e-02 3.777 0.000161 ***
## x11 7.373e+07 2.098e+07 3.514 0.000444 ***
## x8 1.293e-01 4.238e-02 3.052 0.002284 **
## x21 4.140e-02 1.200e-02 3.450 0.000564 ***
## x14 -2.510e-01 9.185e-02 -2.733 0.006303 **
## stat41 -1.941e-01 6.983e-02 -2.780 0.005456 **
## stat4 -1.752e-01 7.060e-02 -2.482 0.013094 *
## stat23 1.773e-01 6.985e-02 2.538 0.011175 *
## stat3 1.638e-01 7.056e-02 2.321 0.020317 *
## stat60 1.712e-01 7.052e-02 2.428 0.015225 *
## stat100 1.786e-01 7.041e-02 2.536 0.011224 *
## stat144 1.631e-01 7.004e-02 2.328 0.019926 *
## stat33 -1.508e-01 7.023e-02 -2.147 0.031820 *
## stat200 -1.590e-01 6.934e-02 -2.292 0.021916 *
## stat149 -1.445e-01 7.087e-02 -2.039 0.041492 *
## x13 4.313e-02 2.121e-02 2.034 0.042026 *
## stat26 -1.414e-01 7.022e-02 -2.014 0.044031 *
## stat24 -1.422e-01 7.034e-02 -2.022 0.043259 *
## stat151 -1.454e-01 7.107e-02 -2.046 0.040845 *
## stat175 -1.452e-01 7.068e-02 -2.055 0.039970 *
## stat126 1.233e-01 7.028e-02 1.755 0.079275 .
## stat146 -1.279e-01 7.045e-02 -1.815 0.069594 .
## stat92 -1.222e-01 7.067e-02 -1.730 0.083756 .
## stat22 -1.186e-01 7.076e-02 -1.677 0.093677 .
## stat205 -1.192e-01 6.968e-02 -1.710 0.087251 .
## stat135 -1.155e-01 7.048e-02 -1.639 0.101352
## stat25 -1.165e-01 7.033e-02 -1.656 0.097706 .
## stat73 1.197e-01 7.124e-02 1.680 0.092979 .
## stat55 1.186e-01 7.025e-02 1.689 0.091357 .
## stat46 1.277e-01 7.060e-02 1.809 0.070532 .
## x19 7.876e-02 4.690e-02 1.679 0.093132 .
## stat84 -1.109e-01 7.081e-02 -1.567 0.117186
## stat19 1.139e-01 7.035e-02 1.620 0.105334
## stat217 1.080e-01 7.036e-02 1.535 0.124756
## stat76 1.050e-01 7.071e-02 1.485 0.137679
## stat13 -1.025e-01 7.004e-02 -1.464 0.143336
## stat156 1.041e-01 7.080e-02 1.471 0.141423
## stat104 -1.014e-01 7.019e-02 -1.444 0.148732
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.412 on 5954 degrees of freedom
## Multiple R-squared: 0.2353, Adjusted R-squared: 0.2293
## F-statistic: 38.98 on 47 and 5954 DF, p-value: < 2.2e-16
##
## [1] "Time taken for Stepwise Selection: 1.76369668245316"
## [1] "Number of data points that have Cook's D > 4/n: 304"
## [1] "Number of data points that have Cook's D > 1: 0"## 3167 2628 2824 3867 6081
## 7.159191e-05 1.074719e-03 9.887038e-06 1.028547e-03 2.809431e-06
## 3220 4244 8540 1169 2211
## 4.430627e-05 1.417519e-04 1.117409e-05 6.985970e-05 2.334567e-06
## 6546 4289 1976 8380 2866
## 2.855587e-06 1.596671e-04 9.023501e-05 2.007446e-05 1.391683e-04
## 3788 8053 9864 416 9047
## 2.345233e-04 1.498815e-05 3.359602e-05 1.874353e-04 1.274449e-04
## 9999 5828 295 6445 2207
## 1.309705e-04 8.139842e-06 2.583671e-05 1.347702e-03 1.914706e-03
## 7690 9633 4140 663 3196
## 5.085519e-05 6.409062e-04 1.551198e-05 1.252944e-05 1.922242e-04
## 2840 7120 90 4490 6380
## 3.427898e-05 1.147433e-04 1.021303e-04 3.693714e-05 1.180759e-04
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## 8.647228e-06 7.590237e-05 6.042832e-07 4.506215e-04 8.931784e-05
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## 1.483293e-04 1.360221e-05 3.555618e-05 4.052754e-05 4.429872e-04
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## 1.092394e-05 3.666000e-05 4.019385e-06 5.501579e-06 2.461734e-05
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## 1.356209e-03 4.947299e-04 1.034814e-04 2.550741e-05 5.546602e-05
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## 6387 9932 1900 7956 7930
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## 4150 8404 6357 9354 5086
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## 7674 3460 7267 7475 516
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## 335 124 5953 8384 2638
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## 16 906 4247 5719 5037
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## 511 3852 6669 5657 782
## 1.080458e-05 1.193176e-03 1.451776e-04 2.244800e-05 6.608346e-05
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## 6783 6595 5474 7203 4631
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## 1478 9824 1994 5816 7524
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## 7015 9451 6306 4625 9713
## 1.169060e-05 1.767966e-04 1.060878e-05 6.075837e-05 3.219084e-05
## 1244 271 3235 1540 4149
## 5.886956e-04 1.206538e-05 1.009449e-05 2.887218e-06 3.383088e-04
## 5315 9017 1903 1239 2010
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## 4476 9389 7012 3583 2161
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## 5518 8454 1984 7763 1078
## 6.746633e-04 5.432370e-07 3.976218e-04 5.257018e-09 3.147213e-06
## 9929 3340 6069 6106 6174
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## 5614 3682 809 825 7777
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## 9592 7461 887 5718 4384
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## 7952 797 4269 4955 9426
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## 2430 3690 4623 9099 6901
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## 8777 7718 6092 4854 2478
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## 4.879531e-05 1.146128e-06 3.841047e-05 3.011029e-06 1.320628e-04
## 6705 2082 9755 8263 4011
## 2.165904e-06 4.104152e-04 7.697785e-05 2.818075e-05 2.408399e-05
## 4278 141 7281 9360 9954
## 1.101700e-04 4.878747e-05 2.584430e-04 1.305608e-05 1.508978e-03
## 7671 7533 5309 5674 4765
## 1.001771e-03 1.318559e-06 6.439967e-05 6.817975e-04 3.855512e-05
## 8324 4757 841 6883 4949
## 2.074281e-04 3.484290e-04 5.125379e-04 4.397010e-03 2.311646e-05
## 938 8166 2893 6031 5836
## 2.641762e-05 2.066283e-04 2.996305e-05 2.988577e-07 8.549078e-05
## 5463 1055 8325 453 695
## 7.868807e-05 9.846559e-05 7.661189e-06 6.068938e-05 2.978231e-06
## 401 6096 9157 4693 432
## 4.308728e-04 9.249075e-05 2.451961e-05 5.200432e-04 1.942161e-06
## 5858 3495 3680 1742 6688
## 3.150835e-05 1.572568e-04 1.812501e-07 4.394184e-06 8.004566e-04
## 111 8958 5537 2561 1558
## 3.620616e-05 2.005901e-04 3.979524e-05 2.048952e-06 2.169809e-04
## 7828 4372 9147 9219 9582
## 3.939773e-04 3.494505e-04 1.035459e-05 1.644242e-04 6.481027e-06
## 7387 3492 5169 8407 8072
## 3.074202e-06 8.311519e-04 1.743247e-03 1.125848e-05 3.816837e-04
## 862 3148 3792 4731 7567
## 7.514644e-04 5.473944e-04 3.965038e-08 3.120450e-05 1.763867e-04
## 9280 6687 4025 8163 2035
## 1.654968e-04 5.961723e-07 8.917325e-07 6.515817e-05 2.200455e-07
## 3145 7505 949 1804 8146
## 6.586666e-06 1.567613e-04 7.056084e-05 4.812377e-04 7.678725e-06
## 8469 5583 8249 1808 1913
## 1.033303e-04 5.191222e-05 4.038018e-05 4.337867e-05 1.295294e-04
## 1411 4147 7056 8112 1464
## 1.760206e-05 4.428368e-05 2.193440e-04 1.265337e-04 2.530757e-04
## 125 3617 2195 6568 2190
## 2.333605e-04 3.083574e-05 1.426049e-04 8.690914e-07 5.680401e-07
## 292 1151 7061 5119 4659
## 6.944290e-06 3.457519e-05 8.224821e-05 1.106065e-04 3.086728e-06
## 7376 1405 9653 4821 9142
## 1.006080e-04 2.489975e-04 7.767013e-05 6.276588e-04 2.597125e-05
## 4975 5911 4666 4537 9241
## 5.512629e-05 7.577903e-05 5.096358e-04 2.951714e-07 4.439645e-04
## 8938 7814 5648 3851 7975
## 3.638781e-04 2.460153e-04 2.062945e-03 5.687971e-05 4.745021e-04
## 3935 3706 3755 6991 3140
## 4.447541e-05 8.687362e-06 1.610718e-04 7.010821e-05 1.628441e-07
## 7288 2664 9842 6667 1713
## 1.374348e-04 4.649516e-04 9.449775e-06 1.044333e-04 3.462035e-06
## 856 6121 6990 246 7854
## 2.536190e-05 3.698034e-06 1.177478e-04 6.285545e-04 1.002723e-05
## 1203 9104 5804 9794 6672
## 5.489846e-04 3.746024e-05 1.937921e-04 1.543618e-04 8.981117e-04
## 9350 5998 5301 6165 1254
## 1.379556e-04 5.411214e-05 8.116374e-06 4.732937e-05 2.443130e-04
## 980 3887 7635 5692 2619
## 3.834855e-08 3.993231e-05 3.227641e-06 1.270688e-07 1.382715e-03
## 4541 7384 1211 8598 1886
## 1.351722e-04 2.413509e-06 1.955060e-04 1.787686e-04 2.452592e-05
## 7165 681 8957 4233 7862
## 6.316777e-05 1.793050e-06 7.446421e-08 1.434451e-05 4.449292e-05
## 3982 9812 7444 7152 6963
## 8.625514e-05 2.150444e-04 5.018255e-04 2.950919e-04 1.799716e-05
## 4460 8556 6749 1073 5896
## 1.827243e-04 8.132010e-05 5.712765e-04 1.794841e-03 7.530635e-05
## 7262 184 4442 3479 5515
## 1.550018e-04 1.480519e-04 2.763788e-04 3.781691e-06 6.010081e-04
## 3385 8785 7467 7757 441
## 5.577341e-05 1.505594e-04 1.793337e-03 4.164837e-05 1.050673e-03
## 8885 9611 1437 7215 9302
## 1.728132e-05 1.133147e-04 5.791191e-04 9.793138e-04 8.874491e-06
## 4270 7890 5681 1864 8467
## 5.258742e-05 2.470982e-04 1.528055e-04 2.529084e-05 1.321011e-05
## 4108 6243 6962 760 5303
## 1.223075e-05 1.905959e-05 7.775433e-05 1.535447e-05 1.132486e-04
## 1081 7460 2475 2663 2456
## 7.601478e-05 8.632708e-06 7.687233e-05 1.914906e-04 1.055392e-04
## 240 8739 7163 8179 6867
## 2.209821e-05 3.194728e-05 3.343268e-08 2.755990e-05 3.507949e-05
## 1047 9213 1402 8880 778
## 1.218823e-04 1.355244e-06 1.956871e-04 7.761333e-05 1.977167e-04
## 8337 3368 1781 4714 2788
## 6.878661e-05 5.310520e-05 9.438497e-07 1.479211e-04 1.779301e-04
## 3898 8327 3455 5952 3964
## 5.387950e-05 6.435921e-06 3.294544e-05 3.645468e-03 9.170877e-06
## 5124 5909 665 4309 7904
## 3.529662e-05 4.036956e-05 8.411530e-05 8.187167e-05 8.264343e-05
## 387 2481 2493 7086 7784
## 4.168704e-06 7.787218e-04 7.840972e-04 2.815527e-06 4.739538e-05
## 634 5936 6384 7495 5801
## 2.672463e-06 9.849917e-06 7.697243e-06 1.359510e-04 2.689007e-05
## 2107 8769 5340 1619 8206
## 2.388845e-04 8.229634e-05 4.201057e-05 3.456172e-06 2.344304e-04
## 134 9928 7073 5545 1331
## 1.520324e-04 2.340906e-05 1.173915e-04 2.888451e-03 3.524976e-05
## 4513 5194 4662 390 6624
## 8.120917e-05 4.843787e-04 9.912050e-05 3.390946e-05 5.547421e-05
## 6805 4394 8182 1280 5734
## 1.271009e-05 9.727444e-07 2.294714e-07 1.288602e-04 4.636550e-04
## 1928 5382 229 3155 7104
## 2.731349e-04 2.780252e-04 1.833037e-03 1.361488e-05 9.569762e-05
## 5882 2144 119 4639 550
## 7.129544e-07 2.625617e-04 5.015687e-04 1.016474e-06 8.263689e-04
## 9982 9442 9939 9423 8447
## 2.622352e-04 9.284124e-06 2.344525e-04 9.809814e-05 1.534083e-06
## 5305 8253 8770 8517 5571
## 2.881092e-05 2.876315e-06 9.952697e-07 1.032316e-04 1.879415e-05
## 8090 2125 9168 2219 320
## 4.079865e-04 1.568815e-05 8.627843e-05 7.099502e-05 2.293727e-05
## 8188 7085 6913 9738 3440
## 9.385934e-05 3.773140e-05 1.956310e-04 3.842554e-05 7.682434e-04
## 4742 1172 5090 5699 2569
## 1.351463e-05 4.834020e-04 1.494321e-04 1.628362e-04 8.091393e-04
## 7259 5050 9406 325 4614
## 3.881474e-06 2.730628e-05 1.131288e-04 7.525933e-05 5.979278e-04
## 6486 8264 7064 2157 4960
## 8.694219e-04 2.304657e-05 8.094092e-05 1.869457e-05 1.390375e-04
## 8930 1927 2423 8131 4929
## 3.208887e-04 4.015930e-05 6.683816e-05 1.107127e-04 1.462899e-04
## 3349 5973 8189 7941 7983
## 3.228314e-05 3.144340e-06 6.928934e-05 5.878467e-05 9.335007e-04
## 2415 6009 404 4373 2324
## 1.836640e-05 2.122596e-05 2.167670e-06 2.585293e-06 1.011108e-04
## 8465 8362 6897 2867 9591
## 2.872576e-04 1.007313e-03 5.065120e-05 5.774295e-05 9.698783e-05
## 5745 8340 3286 1488 4672
## 1.036324e-05 1.303889e-06 5.790988e-08 8.495454e-06 1.715359e-06
## 2189 6506 7111 6719 4410
## 1.239483e-04 5.429715e-05 3.996223e-07 2.003658e-05 5.706057e-06
## 36 8791 1207 2897 1235
## 6.223617e-04 3.178745e-04 4.016804e-05 6.771072e-06 1.179790e-05
## 235 8200 53 3605 2041
## 3.407328e-04 1.521620e-04 2.125899e-04 4.967148e-05 1.048239e-06
## 3837 8170 9124 2334 2892
## 1.135051e-04 2.575293e-04 2.471720e-05 9.836279e-05 2.053715e-04
## 2789 6712 6889 210 7659
## 4.669199e-06 7.349331e-05 2.416410e-05 5.147348e-05 6.150745e-04
## 5551 4953 6039 3262 3981
## 2.394873e-05 7.476029e-04 4.667235e-04 2.426332e-06 9.896805e-05
## 740 357 1646 3497 1030
## 7.691971e-04 1.497731e-04 2.976282e-07 2.290811e-04 2.535033e-05
## 8945 6611 1822 6752 7749
## 9.862888e-05 2.058648e-04 1.036139e-04 1.723124e-05 7.562426e-07
## 195 1687 8725 101 5222
## 3.452500e-06 8.814038e-05 5.046245e-05 1.607359e-05 4.278791e-06
## 9585 6622 3017 1129 764
## 6.564091e-06 5.101039e-05 6.242054e-06 1.835098e-05 9.361769e-05
## 5807 7634 1068 9441 6537
## 3.260509e-04 6.641778e-04 6.007942e-04 8.326309e-05 2.336843e-04
## 129 8910 1559 8452 4577
## 4.177294e-04 2.109954e-04 2.169024e-04 1.806626e-04 4.781011e-05
## 1508 5056 4852 4694 3810
## 2.507173e-05 4.830824e-05 1.359484e-05 1.215350e-04 1.339692e-04
## 789 3518 2135 9048 1233
## 7.556952e-04 2.308158e-06 2.591995e-05 9.392619e-08 2.052836e-04
## 4997 9245 6609 6716 4369
## 3.047147e-04 7.433122e-05 6.264767e-05 1.769789e-05 7.686559e-06
## 3795 3260 4393 5985 7434
## 1.822836e-05 5.533460e-08 1.972118e-05 1.268018e-05 7.064122e-05
## 4718 1950 1309 5976 8165
## 1.982796e-04 1.036087e-04 5.935089e-06 1.286396e-05 9.394161e-05
## 3858 3523 1862 3123 7423
## 2.187966e-04 5.601869e-05 1.832541e-04 1.239523e-06 3.375701e-04
## 6090 5393 7898 1462 2738
## 4.960613e-05 2.467625e-07 1.338937e-05 2.094334e-09 2.801985e-04
## 9615 7385 5272 5358 1807
## 3.013233e-06 3.512757e-04 7.473061e-05 5.585052e-05 6.896533e-05
## 8941 1575 1045 4444 3915
## 1.674226e-05 7.316843e-06 5.827700e-06 6.719271e-07 7.980504e-07
## 4583 6268 6754 1002 9444
## 2.632783e-05 1.791364e-03 1.307503e-04 1.462981e-05 6.146176e-05
## 7049 9872 814 5148 2044
## 1.203251e-05 3.521230e-08 1.961422e-04 1.080544e-04 3.092172e-04
## 8640 853 7129 4884 6037
## 1.862336e-04 3.572274e-05 8.955813e-05 5.598978e-04 1.426785e-04
## 9847 1771 3806 9533 127
## 2.408881e-04 1.500522e-06 7.330952e-05 2.887054e-05 2.327139e-04
## 3315 9757 8223 6247 8152
## 8.926725e-05 2.470848e-05 4.420808e-05 6.798325e-05 4.975570e-05
## 9563 462 128 1496 4882
## 1.802316e-05 6.676936e-04 3.530753e-05 2.657417e-04 2.588053e-06
## 8626 7430 2681 1072 9572
## 2.741857e-04 9.593710e-05 8.549551e-06 2.047719e-04 1.877762e-05
## 5173 4588 6299 6049 6289
## 9.123330e-05 7.767289e-06 3.405601e-04 9.391147e-08 2.914365e-05
## 6932 68 1076 5334 1555
## 5.238979e-06 1.714538e-03 3.654745e-04 1.828193e-06 8.851392e-06
## 1761 5893 6864 736 9546
## 5.947895e-06 4.148903e-05 2.524747e-04 4.695851e-05 7.416681e-06
## 5738 3579 8111 5290 2787
## 7.558458e-06 2.530716e-04 8.191118e-04 5.731805e-06 1.676500e-05
## 572 7871 3515 829 5951
## 2.992562e-05 6.789464e-04 1.647849e-04 2.118960e-05 9.509503e-05
## 587 6116 8516 1390 1548
## 1.172154e-06 1.025910e-04 1.700095e-04 1.900849e-05 5.386285e-05
## 9122 5619 700 9306 5268
## 1.081551e-05 1.668743e-04 1.047543e-05 4.019549e-04 3.084013e-05
## 7309 7661 5350 9149 8093
## 4.013393e-06 8.979673e-05 3.991277e-06 4.263891e-04 7.687312e-05
## 2618 7468 3264 867 350
## 2.799923e-06 1.455115e-06 6.259023e-06 3.051127e-05 4.308905e-04
## 5183 4176 4708 472 422
## 9.601199e-06 4.638076e-04 9.722043e-05 5.974947e-06 4.304382e-04
## 7838 4329 6742 3414 8282
## 4.951821e-04 8.996952e-05 8.857556e-05 8.299995e-06 9.106562e-05
## 5691 6573 9948 3662 8473
## 1.720226e-04 4.036004e-04 3.775368e-05 3.619575e-04 3.669318e-04
## 705 6725 7810 324 3828
## 3.015096e-05 1.259843e-04 1.418596e-04 7.754368e-05 1.154883e-05
## 9870 7695 2387 386 9656
## 1.234949e-04 6.526723e-05 2.159085e-05 3.038133e-05 1.359877e-04
## 7135 3709 4747 1091 4741
## 3.363544e-04 4.653380e-05 6.464955e-05 4.672582e-04 2.894427e-03
## 5398 4415 7127 5670 9664
## 3.555260e-05 4.195193e-05 1.373461e-04 4.412704e-06 7.137510e-05
## 5508 1161 7179 617 3303
## 2.748065e-05 6.354581e-06 6.785317e-05 9.660069e-06 2.023559e-07
## 4954 6321 8373 5603 9461
## 5.223374e-06 1.435577e-04 4.062730e-06 1.626719e-05 6.389077e-05
## 2914 1919 5757 9596 8277
## 5.285987e-07 2.953189e-05 4.858806e-07 1.575319e-04 3.221295e-06
## 3553 9492 3469 8475 2803
## 5.981975e-06 8.154937e-05 1.033198e-04 2.132356e-04 4.116427e-04
## 9277 9547 9947 2126 1888
## 1.436419e-05 7.686387e-04 4.098129e-05 1.563621e-04 9.507231e-08
## 5082 942 8081 167 3289
## 1.583160e-05 2.904504e-05 1.765181e-04 8.884018e-06 1.058172e-04
## 5979 3929 8927 2785 3578
## 2.627345e-04 2.773732e-09 6.668210e-06 1.044267e-03 1.467538e-04
## 6834 4087 2496 3032 3941
## 3.243300e-05 5.371069e-04 2.585779e-05 2.047643e-05 1.320032e-04
## 2692 8453 8478 230 5488
## 1.618844e-05 3.400043e-05 1.133007e-05 4.409396e-06 3.960445e-07
## 5068 6812 4165 5482 6875
## 9.006300e-05 3.348828e-05 1.012751e-04 5.853339e-05 1.409332e-03
## 4409 6949 9495 8194 2168
## 6.032745e-05 8.757397e-05 3.600459e-06 1.377994e-05 5.756573e-05
## 6659 731 3215 310 6409
## 6.375125e-05 3.796386e-04 1.564313e-05 8.209264e-05 6.907587e-05
## 6224 6487 1628 6767 4764
## 1.937558e-05 1.742629e-06 3.782651e-05 9.094661e-04 3.602370e-05
## 9768 6698 7296 7492 7199
## 1.572891e-04 1.093358e-04 2.989597e-06 6.720535e-05 8.700824e-04
## 6105 9984 6423 9307 3601
## 4.324477e-05 1.309260e-04 2.293744e-05 2.108842e-05 8.069882e-05
## 6288 9795 7573 7525 7892
## 1.623524e-04 9.750423e-05 4.307650e-05 8.936173e-06 1.324786e-05
## 7072 8352 1565 6751 8097
## 1.139045e-05 5.093589e-05 1.829492e-05 2.523297e-05 5.033983e-05
## 5610 5431 9199 2060 7883
## 2.102531e-05 8.268705e-05 1.190685e-04 4.075994e-05 8.775814e-06
## 3833 4941 3861 1556 9407
## 8.031379e-05 3.853099e-04 5.030814e-05 4.953196e-04 1.334170e-05
## 668 2520 7047 1444 2689
## 5.943852e-06 2.844726e-05 4.532681e-05 2.045301e-04 8.660498e-05
## 9829 4518 5316 1362 6985
## 1.666777e-04 1.899002e-07 2.090670e-04 1.199198e-06 2.606644e-05
## 655 630 5147 7644 3422
## 8.692487e-05 3.042970e-05 1.108549e-03 2.765714e-07 5.593485e-05
## 820 6836 8566 1809 4938
## 8.200386e-06 5.071290e-05 9.413286e-06 4.363849e-05 1.326071e-05
## 9810 7070 8015 7398 6262
## 2.845397e-07 1.066559e-05 6.011152e-06 1.070574e-04 2.898281e-04
## 1198 1260 1110 599 2155
## 2.746541e-04 1.706455e-05 1.951152e-04 1.302263e-04 2.626032e-04
## 2143 6520 3955 6012 2299
## 9.812228e-07 1.761792e-05 1.205505e-06 3.024416e-05 7.416188e-05
## 6887 147 7923 6721 1934
## 6.234360e-05 7.641117e-05 1.257858e-05 2.648516e-04 1.230825e-04
## 4580 5550 418 5581 1382
## 1.684806e-04 6.480420e-05 1.075899e-04 3.343015e-05 1.870488e-05
## 765 913 7008 3819 9176
## 1.654818e-05 2.082786e-04 1.204827e-04 1.026750e-03 8.248950e-06
## 8361 5626
## 6.116611e-05 5.667101e-05Test
if (algo.stepwise == TRUE){
test.model(model.stepwise, data.test, "Stepwise Selection")
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 110.2 122.2 125.8 125.7 129.3 140.9
## [1] "Stepwise Selection Test MSE: 95.4636497886549"
Stepwise Selection (w/ filtered train)
Train
if (algo.stepwise == TRUE){
t1 = Sys.time()
model.stepwise2 = step(model.null2, scope=list(upper=model.full2), data = data.train2, direction="both", trace = 0)
print(summary(model.stepwise2))
#saveRDS(model.forward,file = "model_stepwise.rds")
t2 = Sys.time()
print (paste("Time taken for Stepwise Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.stepwise2, data.train2)
}##
## Call:
## lm(formula = y3 ~ sqrt.x18 + x7 + stat98 + stat110 + x9 + x4 +
## x16 + x17 + x10 + stat14 + x11 + x8 + stat60 + x21 + stat23 +
## stat41 + stat3 + stat146 + x13 + stat4 + stat149 + stat128 +
## stat100 + stat144 + stat172 + stat24 + stat85 + stat38 +
## stat13 + stat33 + stat35 + stat15 + stat175 + stat11 + stat135 +
## stat61 + stat26 + stat126 + stat84 + stat92 + stat90 + stat207 +
## x19 + stat59 + stat99 + stat105 + stat87 + stat73 + stat50 +
## stat182 + stat54 + stat156 + stat32 + stat76 + x5 + stat153 +
## stat200 + stat177 + x14 + stat210 + stat34 + stat21 + stat174 +
## stat39 + stat162 + stat55 + stat216 + stat115 + stat9 + stat71 +
## stat133 + stat217, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.3366 -5.0809 -0.8976 4.6281 22.0153
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.391e+01 1.965e+00 42.697 < 2e-16 ***
## sqrt.x18 7.100e+00 2.117e-01 33.545 < 2e-16 ***
## x7 3.159e+00 1.436e-01 21.995 < 2e-16 ***
## stat98 9.372e-01 5.480e-02 17.104 < 2e-16 ***
## stat110 -8.874e-01 5.549e-02 -15.991 < 2e-16 ***
## x9 8.437e-01 7.494e-02 11.257 < 2e-16 ***
## x4 -1.353e-02 2.033e-03 -6.653 3.14e-11 ***
## x16 2.976e-01 4.815e-02 6.181 6.80e-10 ***
## x17 4.300e-01 7.340e-02 5.858 4.95e-09 ***
## x10 4.214e-01 6.940e-02 6.072 1.35e-09 ***
## stat14 -2.919e-01 5.524e-02 -5.284 1.31e-07 ***
## x11 8.430e+07 1.665e+07 5.062 4.29e-07 ***
## x8 1.326e-01 3.368e-02 3.938 8.32e-05 ***
## stat60 2.377e-01 5.604e-02 4.242 2.25e-05 ***
## x21 4.201e-02 9.544e-03 4.402 1.09e-05 ***
## stat23 1.997e-01 5.562e-02 3.590 0.000333 ***
## stat41 -2.122e-01 5.531e-02 -3.837 0.000126 ***
## stat3 2.085e-01 5.606e-02 3.720 0.000201 ***
## stat146 -1.867e-01 5.587e-02 -3.342 0.000836 ***
## x13 5.937e-02 1.684e-02 3.524 0.000428 ***
## stat4 -1.911e-01 5.617e-02 -3.403 0.000670 ***
## stat149 -1.747e-01 5.642e-02 -3.096 0.001970 **
## stat128 -1.588e-01 5.545e-02 -2.863 0.004207 **
## stat100 1.856e-01 5.600e-02 3.314 0.000926 ***
## stat144 1.668e-01 5.548e-02 3.006 0.002656 **
## stat172 1.471e-01 5.589e-02 2.632 0.008507 **
## stat24 -1.430e-01 5.585e-02 -2.560 0.010500 *
## stat85 -1.254e-01 5.563e-02 -2.254 0.024234 *
## stat38 1.290e-01 5.584e-02 2.310 0.020923 *
## stat13 -1.150e-01 5.550e-02 -2.073 0.038250 *
## stat33 -1.330e-01 5.582e-02 -2.383 0.017223 *
## stat35 -1.428e-01 5.614e-02 -2.544 0.010971 *
## stat15 -1.106e-01 5.541e-02 -1.995 0.046041 *
## stat175 -1.149e-01 5.605e-02 -2.049 0.040495 *
## stat11 -1.202e-01 5.601e-02 -2.147 0.031855 *
## stat135 -1.220e-01 5.585e-02 -2.185 0.028955 *
## stat61 -1.266e-01 5.587e-02 -2.267 0.023452 *
## stat26 -1.092e-01 5.577e-02 -1.958 0.050257 .
## stat126 1.016e-01 5.585e-02 1.819 0.068968 .
## stat84 -1.131e-01 5.616e-02 -2.014 0.044025 *
## stat92 -1.109e-01 5.601e-02 -1.979 0.047814 *
## stat90 -1.203e-01 5.604e-02 -2.147 0.031855 *
## stat207 1.207e-01 5.593e-02 2.159 0.030912 *
## x19 7.378e-02 3.727e-02 1.980 0.047780 *
## stat59 8.989e-02 5.588e-02 1.609 0.107780
## stat99 9.746e-02 5.651e-02 1.725 0.084625 .
## stat105 1.096e-01 5.554e-02 1.973 0.048524 *
## stat87 -9.329e-02 5.590e-02 -1.669 0.095180 .
## stat73 9.508e-02 5.647e-02 1.684 0.092261 .
## stat50 8.895e-02 5.534e-02 1.607 0.108024
## stat182 9.627e-02 5.635e-02 1.708 0.087610 .
## stat54 -8.949e-02 5.634e-02 -1.588 0.112233
## stat156 9.381e-02 5.614e-02 1.671 0.094790 .
## stat32 -8.847e-02 5.616e-02 -1.575 0.115216
## stat76 9.296e-02 5.607e-02 1.658 0.097387 .
## x5 1.134e-01 6.687e-02 1.696 0.089957 .
## stat153 9.269e-02 5.652e-02 1.640 0.101090
## stat200 -8.860e-02 5.504e-02 -1.610 0.107511
## stat177 -9.132e-02 5.627e-02 -1.623 0.104634
## x14 -1.174e-01 7.281e-02 -1.612 0.106986
## stat210 -8.955e-02 5.613e-02 -1.595 0.110660
## stat34 9.205e-02 5.577e-02 1.651 0.098872 .
## stat21 -9.355e-02 5.639e-02 -1.659 0.097196 .
## stat174 9.384e-02 5.584e-02 1.681 0.092888 .
## stat39 -9.082e-02 5.536e-02 -1.641 0.100921
## stat162 -8.682e-02 5.541e-02 -1.567 0.117197
## stat55 8.644e-02 5.572e-02 1.551 0.120885
## stat216 -7.898e-02 5.540e-02 -1.426 0.154006
## stat115 8.038e-02 5.574e-02 1.442 0.149341
## stat9 -8.224e-02 5.612e-02 -1.466 0.142818
## stat71 8.108e-02 5.574e-02 1.455 0.145831
## stat133 8.165e-02 5.608e-02 1.456 0.145440
## stat217 7.856e-02 5.583e-02 1.407 0.159407
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.265 on 5635 degrees of freedom
## Multiple R-squared: 0.3352, Adjusted R-squared: 0.3268
## F-statistic: 39.47 on 72 and 5635 DF, p-value: < 2.2e-16
##
## [1] "Time taken for Stepwise Selection: 4.71316968202591"
## [1] "Number of data points that have Cook's D > 4/n: 290"
## [1] "Number of data points that have Cook's D > 1: 0"## 3167 2824 6081 3220 4244
## 1.425119e-04 1.652281e-06 1.290855e-06 2.570917e-05 4.506530e-04
## 8540 1169 2211 6546 4289
## 1.324273e-06 2.052561e-04 4.702307e-06 1.946932e-05 4.410655e-04
## 1976 8380 2866 3788 8053
## 1.793595e-04 4.649745e-05 1.350615e-04 3.755547e-04 5.387286e-05
## 9864 416 9047 9999 5828
## 6.912787e-06 3.695718e-04 1.715859e-04 2.658348e-04 1.909861e-05
## 295 7690 9633 4140 663
## 1.573888e-08 2.093156e-04 1.141115e-03 3.623715e-07 5.053358e-06
## 3196 2840 7120 90 4490
## 3.183457e-04 4.310892e-05 5.411189e-05 7.973132e-05 9.876800e-05
## 6380 967 3004 1799 3419
## 4.332096e-05 1.739601e-05 2.254318e-05 1.896225e-04 1.604934e-04
## 3587 5428 239 5688 7541
## 4.597490e-04 5.175246e-07 2.640911e-05 5.064514e-04 7.078193e-07
## 2251 3825 2835 7938 8698
## 6.737695e-05 6.774233e-04 4.406382e-04 1.659452e-05 2.210764e-04
## 7260 6975 6994 6857 7142
## 5.556631e-04 5.083007e-08 8.118228e-08 2.043698e-04 3.417503e-06
## 194 380 8328 6204 139
## 2.037736e-07 3.323754e-05 2.214685e-04 3.718484e-04 1.349012e-04
## 2906 7989 9096 1831 7750
## 5.010317e-04 5.759630e-05 3.206600e-04 2.212533e-05 1.187844e-04
## 3234 8613 6837 4075 9425
## 2.409676e-04 1.594369e-04 4.686267e-04 1.403182e-05 4.359710e-04
## 8638 6781 7776 6574 5504
## 9.450144e-07 1.026005e-04 7.341751e-04 1.030219e-04 3.455231e-04
## 2176 8304 6554 584 8509
## 1.614151e-06 8.271011e-06 2.258773e-04 4.268222e-04 1.938147e-08
## 9291 8768 2002 5639 7835
## 1.060602e-03 6.663029e-04 1.265222e-05 1.109371e-04 1.355917e-06
## 8466 7308 203 7861 5452
## 6.049013e-05 6.824737e-05 2.432165e-05 4.139198e-05 5.482978e-05
## 6130 9697 2068 8978 8209
## 2.736853e-05 3.811943e-04 2.235501e-04 1.769678e-04 5.511068e-04
## 3410 5215 6525 8052 9686
## 1.930402e-04 1.739717e-04 7.479467e-05 7.489994e-06 4.066110e-05
## 4308 8757 6043 4787 3622
## 7.555659e-05 2.489258e-05 4.088253e-04 1.560258e-05 1.213661e-04
## 2244 4837 5522 3061 526
## 2.062721e-05 3.819289e-04 1.751631e-05 1.091737e-04 1.288281e-04
## 3786 6217 4098 212 9630
## 1.233768e-05 2.513614e-04 1.816143e-04 6.623255e-05 1.558300e-06
## 3005 187 6293 4454 2505
## 2.196032e-04 7.206271e-05 2.191608e-04 2.253039e-04 3.789037e-05
## 14 371 4034 2596 7397
## 1.599125e-05 2.978005e-05 5.211462e-05 1.259124e-04 3.495061e-04
## 7538 1008 343 7313 2953
## 2.344371e-05 4.968766e-04 8.410565e-04 4.224917e-04 5.040597e-06
## 241 8008 9602 3152 8950
## 1.351113e-04 1.070789e-03 3.179113e-05 6.581241e-05 2.545352e-04
## 3087 9676 7848 5327 5763
## 2.166218e-04 2.055947e-04 8.969671e-05 1.125724e-04 7.345040e-05
## 4192 5339 540 8763 9340
## 3.470315e-04 7.223057e-05 9.454618e-05 2.076350e-06 1.528752e-06
## 3074 1134 8708 1589 6084
## 2.653222e-05 1.216252e-04 5.738204e-05 2.299745e-04 1.922220e-05
## 6545 1942 5446 3247 7894
## 2.404861e-04 2.799574e-05 2.050689e-04 3.968480e-04 1.276409e-04
## 3927 4207 3182 9715 9967
## 3.622285e-05 4.400487e-06 2.653545e-04 9.248265e-04 7.546503e-06
## 4100 9817 3655 5413 3266
## 2.309117e-04 7.552944e-05 2.265214e-05 1.415005e-03 7.906000e-05
## 82 9971 5051 8998 2630
## 2.853312e-04 9.063132e-05 1.290751e-05 2.488735e-04 9.708204e-05
## 3224 4129 2719 174 3157
## 1.206132e-03 6.473307e-04 8.531415e-07 9.318437e-04 2.082069e-08
## 4819 9305 3277 2934 8444
## 3.603777e-05 5.914471e-05 1.227803e-03 6.857168e-06 2.144785e-04
## 6684 5770 4435 236 6653
## 1.922783e-05 5.208710e-04 3.365987e-04 5.224972e-06 1.119645e-04
## 8217 2115 9091 91 3233
## 1.281894e-04 8.640794e-06 2.813425e-05 7.985603e-05 3.129956e-04
## 7729 7886 1300 1652 4021
## 6.371355e-06 2.249289e-04 1.694425e-04 8.917898e-05 3.404287e-08
## 3370 4134 3223 5997 581
## 4.284359e-04 4.433926e-06 4.175678e-05 2.700233e-04 4.389073e-05
## 2999 7105 900 3297 4812
## 6.609445e-05 8.671323e-06 1.412506e-03 4.808459e-05 5.157081e-04
## 3590 3608 704 6408 4565
## 3.715556e-05 8.638457e-05 5.406486e-05 5.106004e-04 2.741516e-04
## 3390 9420 9237 6320 2497
## 3.958454e-04 2.304193e-07 3.827477e-04 1.649326e-04 3.928467e-04
## 8697 625 1850 1277 7669
## 1.954889e-04 5.301841e-05 7.645235e-05 7.323684e-04 2.082803e-05
## 1322 5547 2708 2169 3434
## 3.233307e-04 7.755596e-04 5.823549e-05 3.383822e-04 9.485445e-04
## 1674 1752 7337 5067 9326
## 1.676553e-04 1.031084e-05 3.057717e-05 4.904350e-05 1.434394e-04
## 1014 9208 8997 3586 1594
## 1.084213e-05 8.347196e-04 2.502551e-05 5.901813e-06 2.406793e-04
## 3685 6252 7787 2798 5462
## 5.886904e-05 3.493293e-04 2.554868e-04 6.694950e-06 1.588953e-05
## 1877 6101 6175 9087 1067
## 1.565828e-04 6.078304e-04 7.497006e-05 4.435693e-05 7.691843e-05
## 1524 2908 6373 4221 1767
## 6.530578e-07 4.738999e-05 5.758231e-04 1.003252e-04 5.305682e-06
## 5125 9215 5664 5274 3130
## 6.718698e-05 2.833886e-06 4.616386e-04 3.357185e-05 1.269306e-04
## 8855 9765 8424 4886 2857
## 4.480661e-04 1.291461e-04 5.780661e-04 3.734165e-05 7.640611e-06
## 4239 6387 9932 1900 7930
## 5.440113e-05 2.672186e-05 2.391475e-04 5.001346e-04 2.133705e-04
## 1451 4883 5894 9995 9478
## 1.425843e-05 3.536315e-09 2.196482e-05 2.476619e-04 2.252144e-04
## 4150 8404 6357 9354 5086
## 7.211740e-06 6.977974e-05 7.581719e-06 4.634928e-04 6.777984e-05
## 6940 7888 679 1922 1794
## 4.464937e-04 1.075464e-04 4.404872e-04 1.225260e-06 6.660655e-06
## 5092 1579 7449 2120 7926
## 1.496247e-05 2.350189e-04 2.037137e-07 8.151126e-05 9.096744e-07
## 1608 3666 6349 3360 602
## 3.517441e-04 1.806658e-05 6.540285e-05 1.178025e-04 5.001885e-08
## 981 7291 9188 3684 2584
## 3.481779e-05 8.074635e-04 3.889980e-05 3.319309e-04 2.732718e-04
## 7234 8154 7381 7950 2546
## 1.485616e-04 1.679510e-05 8.035341e-06 3.852213e-05 2.791337e-05
## 4482 215 5643 4796 7320
## 2.587611e-04 1.612856e-04 8.392551e-07 3.747398e-05 4.328697e-06
## 4562 7756 9145 3963 8070
## 5.513583e-04 2.671746e-05 1.134762e-03 1.633507e-05 1.751654e-04
## 6763 8688 719 6371 4546
## 2.959707e-05 2.178483e-05 1.259694e-04 6.322581e-05 1.928916e-04
## 1202 6888 7389 2851 6242
## 3.423433e-06 4.190287e-05 6.473615e-04 3.666713e-08 5.174873e-04
## 6377 2972 2151 3460 7267
## 9.996249e-05 1.018675e-04 6.273348e-04 2.199244e-05 2.983703e-05
## 7475 516 4422 2873 1232
## 5.491475e-05 2.342169e-04 9.907175e-05 1.948548e-06 3.368630e-04
## 3117 9120 3780 4563 4093
## 1.326129e-07 8.198102e-08 9.444957e-06 3.813069e-05 2.996380e-06
## 1863 7249 6959 2870 1611
## 1.178909e-04 3.143163e-07 4.442648e-05 1.414897e-05 6.112163e-05
## 2933 6353 3470 4887 1311
## 4.307758e-05 9.905676e-08 4.751628e-05 8.876119e-04 7.994771e-07
## 5521 6407 2046 7482 2952
## 1.356002e-05 4.919278e-05 3.457610e-05 1.021364e-04 5.387297e-04
## 8716 4993 5258 755 4604
## 1.603285e-04 7.919671e-05 1.008737e-06 2.899104e-06 6.536837e-09
## 2831 9558 7727 1610 6364
## 1.059441e-04 1.439020e-04 2.591782e-04 2.395764e-05 5.268035e-06
## 3650 2525 3430 3204 5454
## 2.094792e-04 3.625703e-06 7.104203e-05 9.943735e-05 6.692932e-05
## 7527 7534 7521 3239 8955
## 3.315142e-05 4.560040e-05 1.174192e-04 3.536055e-05 3.003705e-06
## 9070 8719 7648 5233 9097
## 1.502141e-05 1.485034e-06 9.198277e-05 1.478945e-06 1.911223e-04
## 424 1004 2414 857 9997
## 2.637364e-04 2.047987e-04 1.115934e-05 7.024425e-04 6.415809e-05
## 7021 9279 932 7310 9045
## 1.074283e-05 2.225971e-04 7.640686e-04 1.752396e-04 5.477621e-06
## 5715 7051 5579 1101 1349
## 3.947638e-05 1.786332e-05 6.955843e-05 2.431174e-05 4.956593e-04
## 8151 438 38 3468 7598
## 1.232057e-04 2.869860e-05 5.412168e-06 4.193814e-06 5.009257e-04
## 6132 9115 4906 7667 7412
## 3.526003e-04 3.537513e-04 7.570326e-05 1.178974e-06 7.551527e-05
## 9333 9717 9173 5958 6334
## 3.405573e-04 1.371117e-04 2.183571e-05 2.227682e-05 8.810081e-05
## 2314 4360 67 8420 2698
## 1.938191e-05 3.383181e-05 2.327286e-04 3.264167e-04 1.257278e-04
## 7583 54 7413 4893 8029
## 2.529430e-04 5.986897e-04 2.344404e-04 5.649286e-06 1.086652e-04
## 8284 7360 2637 9073 5062
## 2.544886e-04 3.516008e-05 2.109116e-05 9.630864e-04 4.883809e-05
## 4983 2620 763 3212 2744
## 2.046994e-07 3.017192e-04 1.037963e-04 2.611646e-05 2.766275e-05
## 9471 2058 3200 5685 9487
## 1.691639e-05 2.181453e-04 1.114019e-04 8.144297e-06 7.590572e-05
## 29 7811 7851 9121 7999
## 5.909009e-06 5.413301e-05 2.574232e-05 5.698657e-06 2.409881e-04
## 2187 3949 8976 3187 9231
## 3.755937e-08 3.554519e-06 3.926149e-05 7.063740e-05 1.571207e-06
## 6896 4912 9782 5683 1130
## 2.049201e-04 1.251070e-04 1.426194e-04 1.437078e-04 4.456512e-07
## 4466 2843 4170 9815 8986
## 8.111031e-05 1.732369e-04 1.104463e-03 7.257843e-05 9.858603e-05
## 8560 807 9650 749 5014
## 8.361645e-06 1.855115e-07 5.010990e-04 4.722482e-06 1.420917e-04
## 5392 334 6314 5093 8389
## 2.431150e-04 4.050441e-04 4.127843e-04 1.986617e-04 1.527335e-04
## 8542 1630 4692 6872 9463
## 3.875161e-08 3.210858e-04 3.396446e-05 1.306486e-05 1.771060e-08
## 4439 3512 6517 3163 5247
## 2.601802e-04 1.149875e-04 3.090055e-05 2.101090e-06 2.106383e-05
## 8344 3190 124 5953 8384
## 1.184264e-05 8.482690e-06 6.571854e-04 4.053032e-04 5.335411e-05
## 2638 6103 318 4348 9119
## 7.732873e-06 1.435944e-05 1.987930e-04 1.222700e-04 1.519884e-05
## 16 906 4247 5719 5037
## 5.948034e-05 6.632344e-05 2.234427e-04 1.524102e-04 7.499639e-04
## 511 6669 5657 782 4600
## 4.126466e-06 3.123272e-04 9.737365e-06 6.217779e-05 1.136801e-04
## 6376 8917 7588 2962 6595
## 3.153459e-05 7.985922e-04 2.794489e-05 3.972203e-04 2.346813e-04
## 4631 9449 2983 4119 479
## 2.601817e-05 1.114432e-04 4.412753e-04 7.222298e-04 4.007341e-04
## 6507 1478 9824 5816 7524
## 8.277579e-04 2.649746e-05 1.220714e-03 3.043528e-04 4.674518e-04
## 7015 9451 6306 4625 9713
## 1.799549e-05 3.963815e-04 3.418757e-06 1.574541e-04 3.622898e-05
## 1244 271 3235 1540 4149
## 1.179218e-03 8.180172e-06 5.774385e-05 5.043185e-06 6.546576e-04
## 5315 9017 1903 1239 2010
## 1.548563e-04 3.188601e-04 3.900921e-05 1.109517e-04 2.336413e-04
## 4476 9389 7012 3583 2161
## 1.602266e-05 6.522577e-05 1.028822e-05 8.804997e-05 1.146442e-06
## 8454 1984 7763 1078 9929
## 6.865864e-06 6.362420e-04 1.668600e-05 8.243125e-06 9.580877e-07
## 3340 6069 6106 6174 5614
## 5.024576e-04 5.612678e-05 3.039862e-05 3.093374e-04 4.001992e-05
## 3682 809 825 7777 7461
## 1.758394e-04 6.969976e-05 1.697191e-04 8.315127e-04 4.730784e-04
## 887 5718 4384 2091 4668
## 6.695202e-04 1.684482e-06 4.586208e-04 1.012831e-03 2.258054e-06
## 5706 9259 8357 5032 3397
## 9.228132e-05 6.959954e-04 2.273813e-04 2.880405e-04 4.224640e-05
## 7736 1156 6191 8410 7217
## 7.161891e-05 1.106986e-06 8.716323e-05 2.149308e-04 1.364078e-05
## 3386 6894 392 1757 939
## 4.174171e-05 7.643595e-05 9.401427e-05 7.691917e-08 3.882305e-06
## 341 8559 9553 6466 3821
## 1.218513e-04 1.083524e-04 1.467994e-04 7.523414e-04 2.656249e-05
## 5777 4670 2426 797 4955
## 2.639237e-04 3.319659e-04 1.129301e-03 4.704743e-06 2.544085e-04
## 9426 2430 3690 4623 9099
## 3.584788e-05 1.590901e-06 3.794179e-04 4.348518e-04 4.348792e-04
## 8777 7718 6092 4854 2478
## 5.129522e-04 2.469037e-04 3.746895e-05 4.275115e-04 1.782543e-04
## 9502 9170 9019 8323 2772
## 1.216603e-04 6.079104e-05 2.748337e-05 7.973523e-05 1.240258e-04
## 6433 7739 4624 9427 9906
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## 9.094976e-05 3.617265e-04 3.279907e-05 2.618225e-05 7.094210e-04
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## 8.121553e-05 7.770393e-05 2.141943e-05 2.850140e-05 9.756326e-05
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## 2.832843e-04 1.466691e-08 7.590156e-05 1.741850e-05 9.768898e-05
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## 1.647767e-04 2.442968e-05 4.927798e-04 2.121127e-04 3.120098e-04
## 6571 7655 122 9584 2462
## 2.954003e-04 1.765101e-04 9.882991e-06 5.033608e-05 4.342814e-05
## 8812 8619 6303 8543 3143
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## 7084 5574 2726 7274 5533
## 2.011202e-04 1.788891e-05 2.520677e-05 7.302504e-05 1.874241e-04
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## 1.164139e-04 3.494455e-06 7.770058e-07 1.214076e-04 5.425970e-05
## 6456 600 6126 9517 5331
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## 7.538066e-06 9.509810e-04 1.959595e-05 2.641056e-05 4.163213e-05
## 7568 6074 8155 7500 3628
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## 5872 94 4515 743 2237
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## 8254 2186 5616 2344 6740
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## 7345 546 7270 3863 3268
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## 5682 9876 7679 5080 1112
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## 7392 3945 3715 769 8271
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## 1700 5461 8329 5495 3475
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## 9473 8225 4187 4878 4506
## 3.331160e-04 4.317880e-07 6.032616e-06 1.474684e-05 1.007737e-05
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## 6.699574e-06 1.292504e-04 3.580153e-05 2.308951e-04 7.789219e-04
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## 1730 3922 7602 3435 5205
## 1.243892e-05 1.133530e-04 1.361275e-06 2.172471e-05 4.145501e-06
## 558 8644 9205 3100 9412
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## 8300 945 3429 7555 2920
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## 2965 6298 8843 1467 924
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## 2097 3263 4828 8811 8876
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## 8993 1938 6361 2832 220
## 1.549089e-04 1.394958e-05 4.893072e-05 1.362243e-04 3.243609e-05
## 7053 3591 1577 6425 969
## 5.030581e-04 5.160035e-04 2.299328e-06 8.331094e-05 2.328637e-04
## 4696 8745 6494 3896 5988
## 1.279585e-04 3.877686e-06 1.218237e-06 7.727341e-05 2.529465e-05
## 1818 3423 3337 5607 2087
## 1.041018e-04 5.461067e-05 1.396710e-06 2.705301e-04 4.897744e-08
## 4802 8970 8035 5138 2973
## 6.783062e-06 1.493291e-05 1.895319e-04 5.013523e-04 9.642720e-05
## 4260 7618 9514 2659 9201
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## 786 8438 6143 696 8895
## 6.172289e-05 2.047426e-04 2.013084e-06 8.067441e-05 2.182934e-04
## 889 8567 4271 7918 1133
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## 3172 8503 1624 5427 4514
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## 8780 2333 1457 9543 5735
## 2.390520e-05 4.820764e-05 4.424241e-06 9.477906e-05 5.989681e-05
## 5766 4932 9642 9911 4291
## 6.262546e-04 8.549374e-07 3.849754e-05 1.102433e-05 7.474211e-04
## 4553 486 5188 9958 5106
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## 3656 1796 3886 5878 1805
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## 4079 813 8735 9510 7290
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## 2291 1647 209 691 4240
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## 9161 9890 1168 1605 7248
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## 7171 3761 2136 6023 4856
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## 9582 7387 8407 8072 862
## 6.902082e-05 2.015706e-07 4.954672e-05 5.103417e-04 7.462994e-04
## 3148 3792 4731 7567 9280
## 1.018399e-03 5.852927e-07 4.110123e-05 5.572340e-04 1.864777e-04
## 6687 4025 8163 2035 3145
## 9.155354e-06 2.348468e-08 2.823492e-04 5.957006e-07 2.157349e-05
## 7505 949 1804 8146 8469
## 3.244436e-04 4.480934e-05 1.046817e-03 4.319809e-05 2.840679e-04
## 5583 8249 1808 1913 1411
## 6.779152e-05 4.238950e-06 6.732132e-05 8.233564e-05 6.766125e-05
## 4147 7056 8112 1464 125
## 2.206886e-05 2.646815e-04 2.553477e-04 3.620639e-04 4.715885e-04
## 3617 2195 6568 2190 292
## 9.580840e-09 8.593640e-05 6.232592e-06 5.576501e-06 6.202781e-06
## 1151 7061 5119 4659 7376
## 1.128032e-05 1.256722e-04 2.491329e-04 5.189280e-07 3.099457e-04
## 1405 9653 4821 9142 4975
## 5.318440e-04 3.612750e-05 7.832601e-04 6.452279e-05 1.711577e-04
## 5911 4666 4537 9241 8938
## 7.179078e-05 8.082877e-04 1.920624e-05 5.063341e-04 4.373200e-04
## 7814 3851 7975 3935 3706
## 5.534207e-04 1.408850e-04 5.284958e-04 1.345868e-04 7.303648e-05
## 3755 6991 3140 7288 2664
## 1.909311e-04 5.010672e-05 9.399728e-06 3.260781e-04 8.577958e-04
## 9842 6667 1713 856 6121
## 1.850894e-05 1.608169e-04 1.908229e-05 1.156696e-04 6.311655e-06
## 6990 246 7854 9104 5804
## 3.187650e-04 7.639802e-04 1.126321e-05 1.386044e-04 3.416226e-04
## 9794 9350 5998 5301 6165
## 3.319684e-04 1.684891e-04 1.283884e-04 5.340652e-07 4.580361e-05
## 1254 980 3887 7635 5692
## 2.942848e-04 1.837246e-07 1.682085e-05 9.447887e-06 7.993271e-06
## 4541 7384 1211 8598 1886
## 2.870993e-04 3.793452e-06 2.053244e-04 4.040442e-04 3.533430e-05
## 7165 681 8957 4233 7862
## 6.475703e-05 4.574045e-05 3.747831e-07 5.765690e-06 1.241656e-04
## 3982 9812 7444 7152 6963
## 1.478038e-04 3.373023e-04 1.098440e-03 5.053621e-04 3.351266e-05
## 4460 8556 6749 5896 7262
## 3.546110e-04 1.573681e-04 1.041203e-03 1.422304e-04 1.633510e-04
## 184 4442 3479 3385 8785
## 2.729806e-04 7.032986e-04 1.697644e-05 1.195062e-04 1.487482e-04
## 7757 8885 9611 1437 9302
## 1.305288e-04 1.905771e-05 1.810180e-04 7.866059e-04 5.586990e-05
## 4270 7890 5681 1864 8467
## 2.455152e-05 2.206810e-04 2.123895e-04 1.908837e-05 6.993210e-05
## 4108 6243 6962 760 5303
## 2.143787e-05 2.192753e-05 2.401430e-04 4.839378e-05 1.075736e-04
## 1081 7460 2475 2663 2456
## 6.766080e-05 7.733089e-05 1.541931e-04 1.980423e-04 2.589873e-04
## 240 8739 7163 8179 6867
## 9.750376e-05 8.775880e-05 2.461174e-05 4.540648e-05 6.056134e-06
## 1047 9213 1402 8880 778
## 1.055378e-04 1.262570e-06 2.107412e-04 9.541630e-05 1.691297e-04
## 8337 3368 1781 4714 2788
## 4.831285e-05 2.394761e-04 8.178099e-07 1.043489e-04 2.351179e-04
## 3898 8327 3455 3964 5124
## 1.298476e-04 1.690792e-07 6.613800e-05 1.290660e-04 1.343610e-04
## 5909 665 4309 7904 387
## 1.612231e-04 1.200992e-04 5.382730e-05 2.174462e-04 4.070999e-05
## 7086 7784 634 5936 6384
## 2.320269e-05 5.354561e-05 4.878166e-06 1.103667e-05 1.282770e-05
## 7495 5801 2107 8769 5340
## 2.060955e-04 1.292182e-04 2.854612e-04 5.470626e-05 6.265379e-06
## 1619 8206 134 9928 7073
## 6.148020e-05 4.960810e-04 2.000240e-04 2.885098e-06 2.499884e-04
## 1331 4513 5194 4662 390
## 1.439653e-04 1.265575e-04 7.283468e-04 2.690788e-04 3.094889e-06
## 6624 6805 4394 8182 1280
## 2.201753e-04 1.295294e-07 6.588706e-06 6.631926e-05 1.436856e-04
## 5734 1928 5382 3155 7104
## 9.909667e-04 5.198245e-04 2.661507e-04 1.626478e-05 8.002045e-05
## 5882 2144 119 4639 9982
## 7.081022e-06 4.552921e-04 5.104257e-04 1.032620e-05 3.571514e-04
## 9442 9939 9423 8447 5305
## 1.531579e-07 4.321889e-04 2.061024e-04 1.339705e-07 1.221580e-04
## 8253 8770 8517 5571 8090
## 1.110912e-05 2.018367e-05 1.195835e-04 1.092406e-04 9.901090e-04
## 2125 9168 2219 320 8188
## 1.580396e-05 9.541805e-05 1.189285e-04 5.680495e-05 1.236043e-04
## 7085 6913 9738 4742 1172
## 1.008917e-05 2.571719e-04 3.708473e-05 2.085465e-05 1.235373e-03
## 5090 5699 7259 5050 9406
## 4.243294e-04 3.955999e-04 6.977863e-06 7.097967e-05 2.169701e-04
## 325 4614 6486 8264 7064
## 1.283799e-04 7.672868e-04 1.570053e-03 1.901442e-04 1.585953e-04
## 2157 4960 8930 1927 2423
## 6.500786e-05 3.078586e-04 7.937776e-04 5.375364e-05 1.182637e-04
## 8131 4929 3349 5973 8189
## 8.450394e-05 2.452891e-04 7.679475e-05 3.122171e-07 3.168523e-05
## 7941 2415 6009 404 4373
## 1.047944e-04 1.025363e-05 1.513768e-05 2.032191e-06 1.365564e-05
## 2324 8465 6897 2867 9591
## 7.646788e-05 3.510773e-04 7.353689e-05 1.496332e-04 1.424044e-04
## 5745 8340 3286 1488 4672
## 2.268207e-05 1.623562e-05 2.620590e-05 3.345424e-06 9.691235e-08
## 2189 6506 7111 6719 4410
## 1.693478e-04 7.553272e-05 1.592220e-06 1.317755e-04 4.139220e-05
## 36 8791 1207 2897 1235
## 1.114109e-03 7.280355e-04 4.400030e-05 3.054715e-06 2.346156e-05
## 235 8200 53 3605 2041
## 8.373262e-04 2.491448e-04 1.395079e-04 1.654250e-04 3.028346e-05
## 3837 8170 9124 2334 2892
## 4.012699e-04 3.699876e-04 4.108511e-05 1.000245e-04 3.254934e-04
## 2789 6712 6889 210 5551
## 2.333848e-07 1.085022e-04 2.640919e-05 6.598144e-05 2.368385e-05
## 6039 3262 3981 357 1646
## 9.302506e-04 1.665732e-05 2.191715e-04 1.469229e-04 2.441997e-05
## 3497 1030 8945 6611 1822
## 2.412127e-04 1.422009e-04 1.808285e-04 3.879577e-04 7.685967e-05
## 6752 7749 195 1687 8725
## 2.388068e-06 9.817156e-06 2.254847e-05 9.794062e-05 3.187491e-05
## 101 5222 9585 6622 3017
## 4.359246e-05 2.504968e-07 6.116946e-05 1.069736e-04 4.830437e-05
## 1129 764 5807 7634 1068
## 3.232167e-05 1.859461e-04 3.968259e-04 1.338585e-03 6.500516e-04
## 9441 6537 129 8910 1559
## 6.953092e-05 2.923975e-04 8.540818e-04 3.295846e-04 1.418343e-04
## 8452 4577 1508 5056 4852
## 3.070813e-04 2.667140e-05 7.712248e-06 8.123945e-05 1.739527e-06
## 4694 3810 3518 2135 9048
## 2.123692e-04 1.472557e-04 3.319615e-05 7.112352e-05 1.213627e-05
## 1233 4997 9245 6609 6716
## 3.821571e-04 4.122738e-04 9.935064e-05 6.612629e-05 6.725356e-07
## 4369 3795 3260 4393 5985
## 1.069082e-04 1.632854e-05 6.001801e-07 2.588906e-05 7.488838e-05
## 7434 4718 1950 1309 5976
## 6.112051e-05 3.162585e-04 1.553622e-04 5.726030e-07 3.738327e-05
## 8165 3858 3523 1862 3123
## 1.049410e-04 2.516143e-04 6.752180e-05 1.863995e-04 1.633403e-05
## 7423 6090 5393 7898 1462
## 5.571217e-04 8.216040e-05 9.577549e-06 2.507243e-05 3.661732e-05
## 2738 9615 7385 5272 5358
## 2.692298e-04 1.084990e-07 6.391864e-04 1.440962e-04 9.423175e-05
## 1807 8941 1575 1045 4444
## 4.155404e-05 2.840285e-05 2.232128e-05 4.022200e-05 6.442647e-07
## 3915 4583 6754 1002 9444
## 1.186172e-06 2.512686e-05 2.055561e-04 5.964816e-05 1.531899e-04
## 7049 9872 814 5148 2044
## 5.363527e-06 1.825789e-05 3.111231e-04 1.366478e-04 2.799506e-04
## 8640 853 7129 4884 6037
## 4.692816e-04 1.866416e-04 1.449263e-04 8.492740e-04 2.750170e-04
## 9847 1771 3806 9533 127
## 5.169081e-04 1.483302e-05 5.739043e-05 2.499381e-05 2.080367e-04
## 3315 9757 8223 6247 8152
## 3.712493e-05 2.757268e-05 9.760802e-05 1.390140e-04 8.893307e-05
## 9563 462 128 1496 4882
## 1.232981e-07 7.473929e-04 4.279743e-05 5.635411e-04 5.144382e-06
## 8626 7430 2681 1072 9572
## 5.915891e-04 1.489532e-04 5.830938e-06 3.903333e-04 1.967139e-05
## 5173 4588 6299 6049 6289
## 1.389511e-04 7.779139e-06 7.948144e-04 2.931372e-05 7.309364e-06
## 6932 1076 5334 1555 1761
## 7.621043e-06 5.976835e-04 8.899186e-06 2.977672e-06 2.733949e-07
## 5893 6864 736 9546 5738
## 7.717202e-05 3.871443e-04 1.643331e-04 2.196173e-06 1.821541e-05
## 3579 8111 5290 2787 572
## 4.592765e-04 1.413498e-03 4.270650e-06 2.624045e-08 6.183795e-05
## 7871 3515 829 5951 587
## 1.442224e-03 1.423438e-04 2.299754e-05 2.928501e-04 2.748885e-05
## 6116 8516 1390 1548 9122
## 2.084932e-04 2.812947e-04 6.152815e-06 1.615818e-04 1.158847e-04
## 5619 700 9306 5268 7309
## 3.513708e-04 5.981006e-05 5.480054e-04 8.573702e-05 1.980046e-05
## 7661 5350 9149 8093 2618
## 3.144991e-04 1.166390e-05 6.997969e-04 6.131512e-05 2.499654e-06
## 7468 3264 867 350 5183
## 2.265062e-07 3.281105e-05 7.722422e-05 1.090023e-03 8.708622e-05
## 4176 4708 472 422 7838
## 9.160843e-04 1.141489e-04 1.332010e-05 1.032846e-03 6.394055e-04
## 4329 6742 3414 8282 5691
## 1.643641e-04 9.610335e-05 2.025202e-05 1.800056e-04 3.737664e-04
## 6573 9948 3662 8473 705
## 8.907561e-04 5.489057e-06 7.000163e-04 7.536428e-04 2.409622e-05
## 6725 7810 324 3828 9870
## 1.794578e-04 2.001355e-04 2.687301e-04 5.477263e-06 1.357812e-04
## 7695 2387 386 9656 7135
## 2.117900e-05 1.921066e-06 3.503804e-05 1.499213e-04 7.832309e-04
## 3709 4747 5398 4415 7127
## 2.632579e-05 4.243809e-05 8.894345e-05 6.708293e-05 3.414092e-04
## 5670 9664 5508 1161 7179
## 2.670012e-05 3.544955e-04 1.238964e-05 9.529619e-05 4.463690e-05
## 617 3303 4954 6321 8373
## 5.856312e-05 4.706369e-06 3.052816e-05 2.746362e-04 2.701632e-06
## 5603 9461 2914 1919 5757
## 2.903011e-05 1.513065e-04 1.342753e-07 1.574442e-05 1.027900e-05
## 9596 8277 3553 9492 3469
## 1.673070e-04 2.931420e-05 1.058703e-05 1.450822e-04 1.177206e-04
## 8475 2803 9277 9947 2126
## 3.395106e-04 4.845831e-04 9.713414e-05 7.046224e-05 3.428308e-04
## 1888 5082 942 8081 167
## 5.041664e-06 1.923042e-05 2.257093e-05 1.364672e-04 2.723069e-05
## 3289 5979 3929 8927 3578
## 3.410937e-04 5.518117e-04 6.679832e-06 6.216951e-06 2.961305e-04
## 6834 4087 2496 3032 3941
## 4.315853e-05 5.561822e-04 3.473394e-05 7.473163e-05 1.671873e-04
## 2692 8453 8478 230 5488
## 1.170249e-06 3.844523e-05 1.298601e-05 2.729968e-07 1.030620e-05
## 5068 6812 4165 5482 4409
## 2.031587e-04 9.316984e-05 2.157147e-04 1.266689e-04 1.099305e-04
## 6949 9495 8194 2168 6659
## 2.772688e-04 1.275770e-06 2.428797e-06 1.892978e-04 1.396350e-05
## 731 3215 310 6409 6224
## 5.092507e-04 2.386792e-05 5.623508e-05 9.165587e-05 7.292794e-05
## 6487 1628 4764 9768 6698
## 8.959689e-07 7.043201e-05 1.838908e-05 4.441957e-04 1.700070e-04
## 7296 7492 7199 6105 9984
## 3.786147e-07 1.886268e-04 1.143864e-03 4.624959e-05 1.397919e-04
## 6423 9307 3601 6288 9795
## 1.363250e-05 4.722073e-05 2.724265e-04 2.662178e-04 1.106520e-04
## 7573 7525 7892 7072 8352
## 3.058607e-05 2.521472e-05 1.859860e-05 4.905640e-05 6.608716e-05
## 1565 6751 8097 5610 5431
## 9.768997e-07 4.849293e-05 7.063574e-05 1.306509e-05 1.474951e-04
## 9199 2060 7883 3833 4941
## 2.268710e-04 4.541878e-05 5.554404e-05 1.361287e-04 6.409436e-04
## 3861 1556 9407 668 2520
## 1.148721e-04 8.244938e-04 3.541892e-07 7.992259e-08 3.179860e-05
## 7047 1444 2689 9829 4518
## 5.038135e-05 3.087254e-04 9.888543e-05 1.754189e-04 3.331929e-06
## 5316 1362 6985 655 630
## 3.565978e-04 6.350616e-05 4.693393e-05 6.159448e-05 9.886952e-06
## 7644 3422 820 6836 8566
## 1.230690e-05 6.884252e-05 2.660243e-06 8.379902e-05 5.477803e-06
## 1809 4938 9810 7070 8015
## 6.175958e-05 8.347087e-06 2.325297e-06 8.798024e-05 1.695118e-05
## 7398 6262 1198 1260 1110
## 3.472892e-04 5.509150e-04 6.341471e-04 8.630619e-07 4.176795e-04
## 599 2155 2143 6520 3955
## 2.717991e-04 3.646696e-04 2.067413e-05 2.196389e-05 3.182204e-05
## 6012 2299 6887 147 7923
## 3.001733e-05 1.706701e-04 1.018487e-04 1.294105e-04 6.187259e-07
## 6721 1934 4580 5550 418
## 2.742481e-04 2.188750e-04 8.674066e-05 3.676387e-05 3.343608e-04
## 5581 1382 765 913 7008
## 4.825765e-05 3.055365e-05 9.920936e-05 5.167224e-04 1.478298e-04
## 9176 8361 5626
## 3.326581e-06 6.100859e-05 1.236766e-04Test
if (algo.stepwise == TRUE){
test.model(model.stepwise2, data.test, "Stepwise Selection (2)")
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 108.4 121.1 124.5 124.4 127.9 139.4
## [1] "Stepwise Selection (2) Test MSE: 96.9543210480203"
LASSO Selection
LASSO (w/ full train)
if(algo.LASSO == TRUE){
# Formatting data for GLM net
# you can use model.matrix as well -- model.matrix creates a design (or model) matrix,
# e.g., by expanding factors to a set of dummy variables (depending on the contrasts)
# and expanding interactions similarly.
x = as.matrix(data.train[,feature.names])
y = data.train[,label.names]
xtest = as.matrix(data.test[,feature.names])
ytest = data.test[,label.names]
grid=10^seq(10,-2, length =100)
model.LASSO=glmnet(x,y,alpha=1, lambda =grid)
cv.out=cv.glmnet(x,y,alpha=1) # alpha=1 performs LASSO
plot(cv.out)
bestlambda<-cv.out$lambda.min # Optimal penalty parameter. You can make this call visually.
lasso.pred=predict (model.LASSO ,s=bestlambda ,newx=xtest)
testMSE_LASSO = mean((ytest-lasso.pred)^2)
print (paste("LASSO Test RMSE: ",testMSE_LASSO, sep=""))
print(coef(model.LASSO,s=bestlambda))
plot(ytest,lasso.pred)
}LASSO (w/ filtered train)
if(algo.LASSO == TRUE){
# Formatting data for GLM net
# you can use model.matrix as well -- model.matrix creates a design (or model) matrix,
# e.g., by expanding factors to a set of dummy variables (depending on the contrasts)
# and expanding interactions similarly.
x = as.matrix(data.train2[,feature.names])
y = data.train2[,label.names]
xtest = as.matrix(data.test[,feature.names])
ytest = data.test[,label.names]
grid=10^seq(10,-2, length =100)
model.LASSO=glmnet(x,y,alpha=1, lambda =grid)
cv.out=cv.glmnet(x,y,alpha=1) # alpha=1 performs LASSO
plot(cv.out)
bestlambda<-cv.out$lambda.min # Optimal penalty parameter. You can make this call visually.
lasso.pred=predict (model.LASSO ,s=bestlambda ,newx=xtest)
testMSE_LASSO = mean((ytest-lasso.pred)^2)
print (paste("LASSO Test RMSE: ",testMSE_LASSO, sep=""))
print(coef(model.LASSO,s=bestlambda))
plot(ytest,lasso.pred)
}LASSO calls
Peforming a lasos call is pretty straight forward. GLM-NET peforms 10-fold CV to determine an optimal penalty parameter.
The coefficients are easy to extract and making predictions are straight forward. It is possible to make ASE style plots like we did previously but it takes a little extra programming. See me if interested.
# summary(model.forward)
# summary(model.stepwise)